unit 3 review for common assessment. match the graph of a quadratic function with it’s equation...
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Match the graph of a quadratic function with
it’s equation below:
f(x) = x2 f(x) = -(x+2)2+4 f(x) = (x+2)2-1
Use the Leading Coefficient Test to determine the end behavior of
the graph of the given polynomial function.
1.) f(x) = -x3 + 4x 2.) f(x) = x4 – 5x2 +4
3.) f(x) = x5 - x
5.) f(x) = -2x4 + 2x2
4.) f(x) = x3 – x2 - 2x
Rise Left, fall right Rise left, rise right
Fall left, rise right Fall left, rise right
Fall left, fall right
Determine without graphing, the critical
points of each function.
1.) f(x) = (x + 2)2 - 3 2.) f(x) = -x2 + 6x - 8
Min (-2,-3) Max (3,1)
3.) f(x) = 3x3 - 9x + 5 4.) = x3 + 6x2 + 5x
Min (-.47, -1.13)Max (-3.53, 13.12)Pt. of Inflection (-2,6)
Min ( 1, -1)Max (-1, 11)Pt. of Inflection ( 0 , 5)
5.) f(x) = x4 - 10x2 + 9Min ( -√5, -16)Max (0, 9)Min ( √5 , -16)
f’(x) = 2x + 4 f’(x) = -2x + 6
f’(x) = 9x2 - 9 f’’(x) = 18x
Find the zeros of each polynomial
function.
1.) x2 – 40 = 0 2.) x3 + 4x2 + 4x = 0
3.) x2 + 11x – 102 = 04.) x2 + ¾x + ⅛ = 0
x = 0, -2, -2
x = -17, 6 x = -½, -¼
If you can’t figure it out then use Quadratic Formula
Find the zeros of the polynomial function by factoring.
1.) f(x) = x3 + 5x2 – 9x - 451.) f(x) = x3 + 4x2 – 25x - 100
x = 5, -5, -4
Which of the following is a rational
zero of
f(x) = –2x5 + 6x4 + 10x3 – 6x2 – 9x
+ 4 1, -3, -2, 4, -1 ????
Remember you could use synthetic division or just do p(x) and see if you get a remainder of ZERO
= 0
So 4 is a factor, the others are not
OR
Use synthetic division to divide x4 + x3 – 11x2 – 5x +
30 by x - 2 . Then divide by x + 3 Use the result to find
all zeros of f(x).
x2 x C RSo you are left with: x2 - 5
Then all the zeroes are: -3, , 2
List all possible rational roots, use synthetic division to
find an actual root, then use this root to solve the
equation.
f(x) = 2x4 + x3 – 31x2 – 26x + 24
Hint 4 and -3/2 are roots
2x2 + 6x – 4
USE QUADRATIC FORMULA!!!
Find the number of possible
positive, negative, and imaginary
zeros of: 2,0 positive roots
0 negative roots
P N IP N I
P N IP N I
2
0
0
0
0
2
1 positive root
3,1 negative roots
1
1
3
1
0
2
3,1 positive roots
1 positive root3
1
1
1
0
2
3,1 positive roots
2,0 positive roots
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Use the given root to find the
solution set of the polynomial
equation.p(x) = x4 + x3 – 7x2 – x + 6GIVEN -3 IS A ROOT
Then we can find the rest by factoring:
So the roots are:-3, -1, 1, and 2
Use the given root to find the
solution set of the polynomial
equations
2i 3-iSince 2i is a root, so is -2i
Turn the roots into factors, multiply them together, then use long division
Then factor to find the remaining roots
So the roots are: 2i, -2i, 3, and -4
Since 3-i is a root, so is 3+i
Turn the roots into factors, multiply them together, then use long division
Then factor to find the remaining roots
So the roots are: 3-i, 3+I, 1, and -4
Find the vertical asymptotes, if any, of the graph of each
function.
x = -2, x = 2 x = 4
No vertical asymptote x = -7
Find the horizontal asymptote, if any, of the
graph of
y = 0y = 1
y = 1y = 3x + 3
If a monomial is on bottom then you just break it up.
Otherwise must do long division