midterm review unit 1,2,3a review packets fr

CPA2 Units 1,2,3A Midterm Review Name _________________________ Period _____

Collection of previously published Review Packets from the unit tests on the Midterm. 1

UNIT 1 Please show work and write the final answer on the lines provided.

LT 1: I can simplify and evaluate algebraic expressions. 1. Evaluate

a) – 5𝑦! − 2|𝑥 + 𝑦| for 𝑥 = −5 and 𝑦 = −2. _____________

b) 3(a-4) – 3a2 – (3-2a) for a = -2 _____________

2. Simplify the expression: 3𝑥 − 𝑥 + 𝑦 − 4 𝑦 − 𝑥 _____________ LT 2: I can identify functions and evaluate functions written in function notation. For #1-5, determine whether each relation is a function. 1) 2) 3) 4) 5)

Yes No Yes No Yes No Yes No Yes No For #6-8, determine whether each relation is a function or not, and explain why or why not without using the Vertical Line Test. 6) {(-3,8), (2,4), (-3,-4)} 7) {(-2,-2), (2, 2), (3, 3)} 8) Yes No Why? Yes No Why? Yes No Why?

X 1 2 3 Y 3 3 3



9. Suppose f(x) = 3x + 7 and g(x) = 5 + x + x2 Find each value. Show your work. a. f(-5) b. g(-5) c. 2f(1) + g(4) __________________ __________________ _______________ LT 3: I can simplify and rationalize square roots. 1. Simplify completely. Rationalize denominators if necessary.

a. 2 48 b.

€

10 8 c.

€

5 200 _______________ ______________ _________________

d.

€

317 e.

€

45 f.

€

106

_______________ ______________ _________________

g.

€

16 −10 38 h.

€

11− 55 1111 i.

€

5 710

_______________ ______________ _________________ LT 4 I can solve equations, solve basic inequalities, and graph inequalities on a number line. 1. 9(2d + 6) = 36

_____________ 2. -4(2a - 7) =6(6a – 10) _____________



Solve the following problems. Write your answer on the line provided. 3. Two friends leave the stadium at the same time and go opposite directions. One walks 2.5 mph. After 45 minutes (3/4 an hour), they are 4.32 miles apart. How fast was the other friend walking? _____________ 4. One mega-bus leaves the Walmart plaza at noon and travels at 55 miles per hour. Another mega-bus leaves an hour later and goes opposite direction than the other. At 5pm, they were 415 miles a part. How fast was the second bus traveling? _____________ Solve each inequality and graph the solution on the horizontal number line provided. 5. 14 + 2y > 2(y + 4) 6. 2(m -3) – 5m > m – 7 ________________________ __________________________ LT 5: I can solve compound inequalities and absolute value inequalities 1. 2x < 6 or 3 - x < -2 2. 4x – 2 > 10 and 7 – x > 12

________________________ __________________________



3. 3 > 5 – 2x > -13 4. |7 – 2x| < 24 ________________________ ________________________ 5. 5|4x + 6| - 8 > 30

________________________

LT 6: I can graph linear functions. Graph each equation by hand. 1. a) 5x – 3y = 15 b) y = -4x + 2 c) y+1=3(x+2)



2. a) 4x + y = -4 b) y – 2= ½ (x+4) c) y = ¾ x - 3

3. a) y=2 b) x = y c) y = ¾ x – 3

LT 7: I can graph and apply piecewise functions. Graph the following function.

1. 𝑓 𝑥 =𝑥 + 2, 𝑖𝑓 𝑥 ≤ 02, 𝑖𝑓 0 ≤ 𝑥 ≤ 6𝑥 − 5, 𝑖𝑓 𝑥 > 6

𝑓 −5 =___________ 𝑓 0 =_____________ 𝑓 6 =_____________ 𝑓 9 =____________



2. 𝑓 𝑥 =−2𝑥 − 5, 𝑖𝑓 𝑥 < −3−2, 𝑖𝑓 − 3 ≤ 𝑥 ≤ 5−𝑥 + 8, 𝑖𝑓 𝑥 > 5

3. T. R. Digger works for a landscaping company. He is paid $13.50 per hour for the first 40 hours he works. He receives time and a half pay for every hour after 40.

a. Write a mathematical model expressing the amount of money T. R. earns for working x hours.

b. How much would he earn if he worked 57 hours? ________________________

4. In May 2006, Boro-‐Addison Company supplied electricity to residences for a monthly customer charge of $7.58 plus .8275 cents per kilowatt-‐hour (kWhr) for the first 400 kWhr supplied in the month and .06208 cents per kWhr for all usage over 400 kWhr in the month.

a. Write a mathematical model expressing the fee for using x kWhrs.

b. Would is the feel for using 582 kWhrs?

________________________



LT 8 I can write equations of lines and piecewise functions. 1. Using the line with a slope of -4 and passing through the point (2,-6), answer the questions: Identify the slope of the line: ___________ Write in :

Slope –Intercept Form_________________ Standard Form _________________ Find the ordered pairs for:

x-intercept _________________ y-intercept ___________________

2. Using the line passing through the points (8,3) and (12,11), answer the questions: Identify the slope of the line: ___________ Write in :



3. Using the line passing through the points (-4,7) and (-12,5), answer the questions: Identify the slope of the line: ___________ Write in :



4. Find the slope of the line that passes through the following point. a) (2,10) and (-3, 10) b) (2,8) and (2,5) c) (-1, -2) and (-3, -7)

___________ ____________ _______________ 5. Find the equation of the line in standard form whose graph passes through points (3,-2) and (3,6) __________________________ 6. Find the equation of the line in standard form whose graph passes through points (3,-5) and (1,-5) __________________________ 7. Find the equation of the line in with a slope that is undefined and whose graph passes goes through point (7,2)

__________________________



8.. Write the equation of the piecewise function. The points at (-3, 1) and (2, -1) should be open circles.

𝑓 𝑥 =

9. Write the equation of the piecewise function.

𝑓 𝑥 =

LT 9: I can apply equations of lines to real world problems. 1. Lisa makes candles and sells them. At one craft show she sold 12 candles and made $42. At another show

she sold 22 candles and made $92. a. Write a linear equation in slope-intercept form that represents the amount of money she made as a function

of the number of candles she sold.

________________________ b. What is the slope of your line (include units)? _____________

What is the real-world meaning of the slope? c. What is the y-intercept of your line (include units)? ______________

What is the real-world meaning of the y-intercept? d. If she sells, 10 candles, how much do you expect she would make? ______________ e. If she made $67, how many candles do you think she sold? ______________



2. A college student starts a lawn care business. He charges a flat fee of $5 to cover his travel fees plus $30 for each hour of work.

a. Write a linear equation in slope-intercept form that represents the amount of money he makes as a function

of the number of hours worked.



What is the real-world meaning of the y-intercept? 3. A new airline company, Epsilon Air, starts departing from State College. Instead of charging a flat rate for

each checked bag, they charge by the weight of the bag. Mr. Constable is charged $31 for his 10 pound bag. Mrs. Rupert is charged $43.50 for her 15 pound bag.

a. Write a linear equation in slope-intercept form that represents the cost for checked as a function of the

weight of the bag.



What is the real-world meaning of the y-intercept? d. Ms. Peterson’s checked bag is 13 pounds. How much will she be charged? ______________ e. Mr. Fravel was charged $29.75. How much does his checked bag weigh? ______________



LT 10: I can use linear regression to solve real world problems. 1 . The table below shows the number of oil changes per year and the cost of repairs per year.

Number of Oil

Changes 0 1 2 3 3 4 4 5 6 7 10

Cost or repairs per year

$600 $700 $500 $300 $400 $450 $250 $400 $100 $150 $0

a. Graph the data in your calculator. Then use the calculator to write the equation for the line of best fit. Round to three decimal places.

_______________________________

b. What is the slope of your line (include units)? _____________ What is the real-world meaning of the slope? c. What is the y-intercept of your line (include units)? ______________ What is the real-world meaning of the y-intercept? d. Nancy is changes her oil 8 times a year. Using the equation for the line of best fit, what would you expect her repairs cost per year to be?

______________ e. Rosie has repairs cost of $525. Using the equation for the line of best fit, how many times do you predict that she changes her oil?

______________ 2. The data pairs give the U.S. production of beef from 1990 to 1997, where x is years since 1990 and y billions of pounds of beef.

(0, 22.7), (1, 22.9), (2, 23.1), (3,23.0) (4, 24.4), (5, 25.2); (6, 25.5), (7, 25.5) a. Graph the data in your calculator. Then use the calculator to write the equation for the line of best fit. Round to three decimal places.

__________________________ b. What is the slope of your line (include units)? _____________ What is the real-world meaning of the slope? c. What is the y-intercept of your line (include units)? ______________ What is the real-world meaning of the y-intercept? d. If this trend continues, what would you expect the US production of beef to be in 2000? ____________ e. If this trend continues, when do you expect the production of beef to exceed 30 billion pounds? ________



LT 11: I can solve systems of equations by substitution, elimination, and graphing. Solve the systems by graphing. Write your answer as an ordered pair.

___________ ___________

Solve the systems using the substitution method or elimination method. Write your answer as an ordered pair. 3) 2x + y = 9 4) 3x + 5y = 12 5) x – 9y = 25 3x – 4y = 8 x + 4y = 11 6x – 5y = 3 ___________ ___________ ___________



6) 2x + y = -9 7) 3y - 18 = x 8) 4x + 3y = 1 3x + 5y = 4 4x – 2y = 8 3x + 6y = -3

___________ ___________ ___________ 9) 6x – y = 5 10) 4x + y = 2 11) 4x – 4y = 40

12x – 2y = 3 6x + 3y = 0 3x - 2y = 25

___________ ___________ ___________



UNIT 2A (part 1) You should be able to do this LT WITHOUT a calculator: LT 9: I can perform operations with imaginary numbers. 1. Simplify each expression. If the expression contains a square root, simplify it completely. Write final answers in standard form. A) ! −350 B) !!(−12+2i)+(14−13i)

________________________________ ________________________________ C) !! 9+4i( )– 3−7i( ) D) !!(−5−6i)(6+ i) ________________________________ ________________________________ E) ! −252 F) !!(2−4i)(−3−2i) ________________________________ ________________________________

You should be able to do these WITH a calculator (if you need it): LT 1-‐6: I can factor quadratic expressions. 2. Factor each expression completely. A) !!25x3 −20x2 +10x −8 B) !!12m5 −40m3 C) !!100x2 −49 _________________________________ ________________________ ___________________ D) !!10x2 +31x −14 E) !!9y

3 −49y2 −30y F) !!100x2 −20x +1 _________________________________ ________________________ ___________________



G) !!x4 −81 H) 10x4 −35x3 −12xy+42y I) !!18x2 +48x +32 _________________________________ ________________________ ___________________ LT 7-‐8: I can solve quadratic equations using factoring and square roots. 3. Solve each equation. Show all work. If necessary, simplify all square roots completely. Use fractions instead of decimals when necessary. A) !!2x2 −5x −3=0 B) !!5x2 −27x −3=15

________________________________ ________________________________

C) !!x2 −140=0 D) !!6x2 −13=251 ________________________________ ________________________________

E) !!4x2 +80=0 F) !!5x2 +40= 4

________________________________ ________________________________



LT 10: I can complete the square to solve quadratic equations and write them in vertex form. 4. Solve each equation by completing the square. Show all work.

A) !!x2 +4x −23=0 B) x2 −10x+26=8 ______________________________________ _____________________________________

C) !!10x2 −20x +82=7 D) !!4x2 +8x +80= −4

______________________________________ _____________________________________ LT 12 I can use the discriminant of a quadratic equation to determine the number of

solutions. 5) Find the discriminant of each quadratic equation, then state the number of real and complex solutions. A) −2𝑥! − 8𝑥 − 14 = −6 B) 9𝑥! − 3𝑥 − 8 = −10 C) 5𝑥! − 8 = 10+ 4𝑥 Discriminant: __________ Discriminant: __________ Discriminant: __________ Number/Type of Solutions: Number/Type of Solutions: Number/Type of Solutions:



LT 13 I can write quadratic equations given real solutions. 6) Write a quadratic equation in standard form with given solutions. Show all work. A) x = ½ and x = -‐5 B) x = 6 and x = − 6

________________________________ ________________________________ C) x = 3 and x = − !

! D) x = 3 and x = −3

________________________________ ________________________________

LT 11 I can solve quadratic equations using the quadratic formula. 7) Solve the equation using the quadratic formula. If necessary, simplify all square roots completely. Use fractions instead of decimals when necessary. Show all work.

A) 5𝑥! + 2𝑥 + 1 = 0 B) 𝑥! + 10𝑥 + 34 = 0 ________________________________ ________________________________ C) 6𝑥! + 7𝑥 − 3 = 0 D) 6𝑥! + 4𝑥 + 1 = 0

________________________________ ________________________________



UNIT 2B (part 2) Unit 2-2 Learning Targets:

Modeling with

Quadratic Functions

1. I can identify a function as quadratic given a table, equation, or graph. 2. I can determine the appropriate domain and range of a quadratic equation or event. 3. I can identify the minimum or maximum and zeros of a function with a calculator. 4. I can apply quadratic functions to model real-life situations, including quadratic regression models from data.

Graphing

5. I can graph quadratic functions in standard form (using properties of quadratics). 6. I can graph quadratic functions in vertex form (using basic transformations). 7. I can identify key characteristics of quadratic functions including axis of symmetry, vertex, min/max, y-intercept, x-intercepts, domain and range.

Writing Equations of Quadratic Functions

8. I can rewrite quadratic equations from standard to vertex and vice versa. 9. I can write quadratic equations given a graph or given a vertex and the y-intercept (without a calculator). 10. I can write quadratic expressions/functions/equations given the roots/zeros/x-intercepts/ solutions. 11. I can write quadratic equations in vertex form by completing the square.

PART I: You should be able to do these WITHOUT a calculator. LT 1 I can identify a function as quadratic given a table, equation, or graph. (NC) 1) Identify the function as quadratic or not. a. 𝑓 𝑥 = 𝑥 5𝑥 − 2 − 3𝑥! b. c. 𝑓 𝑥 = 𝑥 6𝑥 + 2 − 6𝑥! Quadratic NOT Quadratic Quadratic NOT Quadratic Quadratic NOT Quadratic d. e. f. Quadratic NOT Quadratic Quadratic NOT Quadratic Quadratic NOT Quadratic



PART II: You should be able to do these with access to a calculator. LT 2 I can determine the appropriate domain and range of a quadratic equation or event. 2) Determine the domain and range for each of the following:

a) The data on the table represents horizontal distance in feet that a baseball travels when hit at various angles. The maximum distance the ball travels is 234 feet.

Angles 20 32 38 46 50 Distance 198 234 225 185 153

Domain: _______________________ Range: _________________________

b) Domain: _______________________ Range: _________________________

LT 3 I can identify the minimum or maximum and zeros of a function with a calculator.

3) The equation h = 10 + 40t – 16t2 describes the height h, in feet, of a ball that is thrown straight up as a function of the time t, in seconds, that the ball has been in the air. At what time does the ball reach its maximum height? ___________________ What is the maximum height? ___________________ When does the ball hit the ground? ___________________ When is the ball 20 feet above the ground? ___________________ 4) The number of dolls a toy company sells can be modeled by −4 p +180 , where p is the price of a doll. a) Write an equation in standard form that represents the revenue the company makes in terms of p.

Revenue = _______________________________ b) What price will maximize revenue? What is the maximum revenue? Answer this question

algebraically, showing all work. Price: _______________________________

Max Revenue: ________________________



5) A triangle has a base of b inches and a height of (-‐3b + 12) inches.

a) Write an equation in standard form that represents the area of the triangle in terms of b.

Area = _______________________________

b) What base length will maximize the area of the triangle? What is the maximum area? Answer this question algebraically, showing all work.

Length: _______________________________

Max Area: ____________________________

LT 4 I can apply quadratic functions to model real-‐life situations. Use the STAT menu of your calculator to find an approximate quadratic regression model. Round the numbers in your equation to 3 decimal places. 6) Data was collected on the income received at various prices of a ticket.

a) y = ______________________________________ b) Find the profit (to the nearest dollar and cent) when the price is $30: _____________________

7) Using the data to answer the questions. a) Does a quadratic function model the data? Why? __________________________________ b) Write the regression equation that models this data. ___________________________________________ c) Estimate the distance the ball would travel if the bat is 55 degrees. ___________________________________________ d) If the ball travelled 200 feet use your model to estimate of the angle of the bat? __________________________________________

Price of ticket in $ 10 25 45 70 90 Profit in thousands of $ 8.5 25.7 38.2 38.8 24.5



8) The profit P from handmade sweaters depends on the price, x, at which each sweater is sold. The function !!P = −x2 +120x −2000 models the monthly profit from sweaters for one tailor.

A) What is the maximum monthly profit determined by this model? Use completing the square. ___________________

B) What prices would result in a profit of $0? ___________________

LT 8 I can rewrite quadratic equations from standard to vertex and vice versa 9) Rewrite the equation into standard form algebraically. Show your work.

a) !!y = 12(x +4)

2 −3 ___________________

b) y =−7(x+5)2 −10

___________________ 10) Rewrite the equation into vertex form using any algebraic method. Show your work. a) y =−3x2 +12x−7

___________________ a) y =2x2 +12x−9

___________________ LT 9. I can write quadratic equations given a graph or given a vertex and the y-intercept (without a calculator).



11) Find the equation of the parabola in vertex form having: Answer this question algebraically a) vertex of !(−3,−4)and a y-intercept of 23. f(x) = ________________ b) vertex: (-2,-2); and passes through point (-1,0) f(x) = ________________ c) vertex (–2,6) and passes through the point (–3,11). f(x) = ________________ LT 10. I can write quadratic expressions/functions/equations given the roots/zeros/x-intercepts/ solutions. 12. Write a quadratic equation in standard form with given roots, zeros, x-‐intercepts or solutions. Show all work. A) ½ and -6 ___________________________ B) 9 and -7 ___________________________

C) 7,− 7 ___________________________

D) 3i and -3i ___________________________ E) 10i and -10i ___________________________ F) 3 5,−3 5 ___________________________



LT 11 I can write quadratic equations in vertex form by Completing the Square. 13) Rewrite each equation into vertex form by completing the square. Then name the vertex. Show all work.

A) y = x2 +4x−23 B) y =4x2 +8x+23 y = __________________________ Vertex: __________ y = ____________________________Vertex: _______

C) y =−x2 −12x+47 D) !!y =2x2 +20x +44

y = __________________________ Vertex: __________ y = ____________________________Vertex: _______ E) y =10x2 −20x−13 F) y =−7x2 −42x+20 y = __________________________ Vertex: __________ y = ____________________________Vertex: _______



PART III: You should be able to do these WITHOUT a calculator. LT 5. I can graph quadratic functions in standard form (using properties of quadratics). LT 6. I can graph quadratic functions in vertex form (using basic transformations). LT 7. I can identify key characteristics of quadratic functions including axis of symmetry, vertex, min/max, y-intercept, x-intercepts, domain and range. 13) Graph each quadratic equation by hand. You should graph at least 5 points before drawing your curve.

A) y =−x2 −4x−3 B) !!y = −12(x +2)

2 +7

Min or Max (circle one) Vertex: ______________ Axis of Symmetry: _____________ y-intercept: _____________________ x-intercepts: ____________________ domain: ______________________ range: _______________________

Transformations: Reflection _________________ Vertical Stretch ______________ Left/Right __________________ Up/Down ___________________ Vertex ________________ Min/Max of _______ at _________ (circle one) y-int ____________



C) y =2x2 −6x−8 D) y =3(x+1)2 −10

Min or Max (circle one) Vertex: ______________ Axis of Symmetry: _____________ y-intercept: _____________________ x-intercepts: ____________________ domain: ______________________ range: _______________________

Transformations: Reflection _________________ Vertical Stretch ______________ Left/Right __________________ Up/Down ___________________ Vertex ________________ Min/Max of _______ at _________ (circle one) y-int ____________



UNIT 3A (part 1) Calculator Section LT 1: I can classify polynomials. 1. Write each polynomial in standard form. Then classify each polynomial by its degree and number of

terms. Finally, name the leading coefficient of each polynomial.

a. b.

Standard Form: _____________________ Standard Form: _____________________ Classify: __________________________ Classify: __________________________ Leading Coefficient: _____ Leading Coefficient: _____ LT 2: I can identify the characteristics of a polynomial function, such as the intervals of increase/decrease, intercepts, domain/range, relative minimum/maximum, and end behavior. 2. Consider the functions graphed below:

Determine the intervals of increase and decrease, the intercepts, the domain and range, and the coordinates of all relative minimums and maximums. Round all answers to three decimal places. a) Intervals of increase: _________________________ Intervals of decrease: _________________________ x-‐intercepts: _________________________________y-‐int _______ Domain: ___________ Range: _______________ Relative Minimum(s): ________________________ Relative Maximum(s): ________________________

b) Intervals of increase: _________________________

Intervals of decrease: _________________________

x-‐ intercepts: _________________________________y-‐int _______

Domain: ___________ Range: _______________

Relative Minimum(s): ________________________

Relative Maximum(s): ________________________

!!8−4x2 −9x3 !!(x2 +6)2



c) Intervals of increase: _________________________ Intervals of decrease: _________________________ x-‐intercepts: _________________________________y-‐int _______ Domain: ___________ Range: _______________ Relative Minimum(s): ________________________ Relative Maximum(s): ________________________

LT 3: I can use polynomial functions to model real life situations and make predictions. 3. The volume of a box has a width of x +1( ) inches. The volume is expressed as a product of the length of its dimensions and is expressed by V (x) = −x3 +3x2 + x −3 . Use synthetic division and the given width to completely factor . Put the dimensions in the blanks. The dimensions of the box are x +1( ) , _____________, and _____________ inches. The maximum volume of the box is ________________. (Use your calculator) 4. The price of a stock can be represented using the following function: 𝑓 𝑥 = 𝑥! − 5. 66𝑥! + 5.1𝑥 + 12.71 where x is the hours 12:00 pm when the stock market opens. Assume the stock market closes at 4:00 pm.

a. What is the maximum price of the stock? How many hours after 12:00 pm does it occur?

_____________

_____________

b. What is the minimum price of the stock? How many hours after 12:00 pm does it occur?

_____________

_____________

c. Will the stock ever be worth $0? How can you tell? _____________

( )V x



5. The data in the table gives the average speed y (in knots) of the Trident motor yacht for different engine speeds (in hundred of revolutions per minutes, or RPMs). Round to 4 decimals.

a. Find a cubic polynomial to fit this data. Is it a good model?

______________________________________________________

b. Estimate the average speed of the Trident for an engine speed of 2400 RPMs. ____________

c. What engine speed produces a boat speed of 14 knots. ___________________________ LT 4: I can write standard form polynomials in factored form and vice versa. 6. Write in standard form.

________________________________

7. Write 𝑦 = 2 𝑥 + 3 !(𝑥 − 1) in standard form. ________________________________ 8. Write in factored form by factoring. ________________________________

!!y = (2x +1)(x −3)(x +5)

!!f (x)=

!!f (x)=

!!y =3x3 +7x2 −15x −35

!!f (x)=



9. Write 𝑦 = 3𝑥! + 24𝑥! − 60𝑥 in factored form by factoring. ________________________________ 10. Write 𝑦 = 𝑥! + 5𝑥! − 36 in factored form by factoring. ________________________________ LT 5: I can find the zeros (or x-intercepts or solutions) of a polynomial in factored form and identify the multiplicity of each zero. 11. Write in factored form by factoring (this is a Learning Target 4 skill). Then name

all zeros and state their multiplicity. Show your work.

________________________________ 12. Name all zeros and state their multiplicity: 𝑦 = 𝑥 + 3 !(𝑥 − 1)𝑥!(𝑥 − 𝜋)! LT 6: I can write a polynomial function from its real roots. 13. Write a polynomial equation with the given zeros. You may leave the equation in factored form. a. 4, -‐1, 6 b. -‐2, -‐6, -‐4 Factored Form: _____________________ Factored Form: _____________________

!!f (x)=

!!f (x)=

!!y = x3 +10x2 +25x

!!f (x)=

!!f (x)= !!f (x)=

Zero(s) Multiplicity

Zero(s) Multiplicity



LT 7, 8, and 9: I can divide polynomials and use the Remainder Theorem to evaluate polynomials. 14. Divide using long division.. Then tell whether the divisor is a factor of the dividend. Show all work. a. Answer: ______________________________ Is the divisor a factor? __________ b. 7𝑥! + 4𝑥 + 2 ÷ 7𝑥 + 4 Answer: ______________________________ Is the divisor a factor? __________ c. 2𝑥! + 8𝑥! − 𝑥! − 4𝑥 + !

!÷ 2𝑥! − 1

Answer: ______________________________ Is the divisor a factor? __________

24x4 + 31x3 + 7x2 + 4x +10( ) ÷ 3x + 2( )



15. Suppose . Divide using synthetic division then answer the following questions. Result of division: __________________________ Find _________ Is -‐3 a zero of ? _______ 16. Suppose 𝑃 𝑋 = 5𝑥! + 2𝑥 − 9

Divide using synthetic division. Then answer the following questions.

(5𝑥! + 2𝑥 − 9)÷ (𝑎 + 2) Result of division: __________________________ Find 𝑃 −2 = _________ Is -‐2 a zero of 5𝑥! + 2𝑥 − 9? _______ 17. Divide 6𝑥! − 𝑥! − 1500𝑥 + 80 ÷ 𝑥 − 4 . Then tell whether the divisor is a factor of the dividend. Show all work. Answer: ______________________________ Is the divisor a factor? __________ 18. Divide 10𝑥! − 225𝑥! + 124𝑥 − 20 ÷ 𝑥 + 5 . Then tell whether the divisor is a factor of the dividend. Show all work. Answer: ______________________________ Is the divisor a factor? __________

P x( ) = −2x4 +14x2 + 6

−2x4 +14x2 + 6( ) ÷ (x + 3)

!!P(−3) −2x4 +14x2 + 6



Non-‐Calculator Section LT 2: I can identify the characteristics of a polynomial function, such as the intervals of increase/decrease, intercepts, domain/range, relative minimum/maximum, and end behavior. 19. Describe the end behavior of the graph of each polynomial function by completing the statements or sketching a. b. c.

x→−∞, f (x)→ _______

x→∞, f (x)→ ________

x→−∞, f (x)→ _______

x→∞, f (x)→ ________

x→−∞, f (x)→ _______

x→∞, f (x)→ ________

20. List the x-‐and-‐y-‐intercepts of and

end behavior. Then sketch a graph of the function.

x-‐intercepts = ____________________

y-‐intercept = _____ Show your work. 21. List the x-‐and-‐y-‐intercepts of y = 2(x-‐1)(x+4)(x+2) and end

behavior. Then sketch a graph of the function. x-‐intercepts = ____________________

y-‐intercept = _____ Show your work.

!!f (x)=7x3 −8x2 +2x !!f (x)= −0.3x

7 −2x4 +2 !!f (x)=2x10 −7x4 +1

y =(x−2)(x+1)(x+5)

As , As ,

As , As ,



UNIT 3B (part 2)

Please review the most recent review packet for the unit 3B test.

midterm review unit 1,2,3a review packets fr

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