Algebra 2 NAME __________________ Chapter 5 Practice Test I. Quadratic Equations 1. What is the standard form of a quadratic equation? __________________

2. What is the vertex form of a quadratic equation? __________________

3. What is the standard form of a complex number? __________________

4. What is the Quadratic Equation? ____________________________

5. Please list the all of the methods to find x-intercepts

II. Graphs of Parabolas (without a calculator) Please sketch the following graphs (show 5 plotted pts.) and answer the corresponding questions.

6. Given:

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y = 2 x − 3( )2 − 5 x y Opens up or down? _______ Vertex:

Maximum or Minimum? (circle one) Axis of Symmetry: ___________

7. Given:

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y = x 2 − 2x − 4 x y Opens up or down? _______ Vertex: Maximum or Minimum? (circle one) Axis of Symmetry: ___________

Algebra 2, Chapter 5 Practice Test page 2 III. Complex Numbers (without a calculator) Please put the following numbers in standard form for complex numbers. Show steps for partial credit. Always reduce fractions and use simplified radical form.

8.

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(4 + 3i) + (2 − 8i) 9.

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−5(2 3 − 3 −2) 10.

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−1218

11.

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(2 − i)(−3 + 4i) 12.

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2 + i1+ 3i 13. (4 + 5i)(4 – 5i)

14.

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2 −98 15.

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−15( ) −3( ) 16.

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6i1− 4i

IV. Solving Quadratic Equations (x-intercepts, zeros, roots) 17. Please solve the following equations by factoring. (GCF, DOTS, PST, or Rainbow!)

a.

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x 2 + 7x +15 = 5

b.

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6x 2 −18x −18 = 6

c.

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7x 2 + 2x = 0

d.

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15x 2 − 3x = 3− 7x

e.

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7x 2 −14x = −7

18. Please solve the following equations by the square root method. Solve for real or complex numbers. (Notice… there is not a “b-term”!)

a.

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2x 2 +144 = 0

b.

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9x 2 +10 = 91

c.

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x 2 − 8 = 12

d.

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10x 2 + 20 = 8x 2 − 4

Algebra 2, Chapter 5 Practice Test page 3 19. Please solve the following equations by completing the square. Solve for real or complex numbers. Please also identify the vertex. Thanks!

a.

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x 2 −10x +18 = 0

b.

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x 2 − 4x = 8

c.

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2x 2 − 8x + 5 = 0

V( , ) V( , ) V( , ) x-int: ________ x-int: ________ x-int: ________ d.

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−x 2 + 2x = 7

e.

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2x 2 + 20 = 6x

V( , ) V( , ) x-int: ________ x-int: ________ 20. Please solve the following equations using the Quadratic Formula. Solve for real or complex numbers.

a.

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x 2 −10x +18 = 0

b.

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x 2 − 4x = 8

c.

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2x 2 − 8x + 5 = 0

d.

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−x 2 + 2x = 7

e.

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2x 2 + 20 = 6x

Algebra 2, Chapter 5 Practice Test page 4 21. Please find the discriminant of the following quadratic equations and put your answer in the first blank. ON the second blank, please state the number of real solutions for the equation. Discriminant # of solutions

a.

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x 2 + 6x = −9 ____________ ____________

b.

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x 2 + 4x = 2 ____________ ____________

c.

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x 2 +16 = 0 ____________ ____________

22. Please use your graphing calculator to find the roots of the quadratic equation. (Please round your answers to two decimal places)

a.

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3x 2 − 4x − 8 = 0

b.

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−2x 2 + 5x +1= 0 __________ __________ __________ __________ IV. Applications 23. Grace is standing on top of a building 70 feet high and wants to throw a ball into a bucket on

the ground. How many seconds will it take the ball to hit the bucket?

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H = −16t 2 + h0( ) 24. The number of holiday packages a resort can sell is modeled by -.15p+90, where p is the price of a holiday package. Revenue is the price times the number of packages sold: R =___________________________ a. What price will maximize revenue? b. What is the maximum revenue?