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Module 11 Revision (Algebra) Quadratic Functions 1.

Solve x² + 2x – 35 = 0. Ⓐ x = –7, 5 Ⓑ x = –5, 7 Ⓒx=–

1 1 , 5 7

Ⓓ x = 5, 7 2.

Determine whether each example represents a linear, exponential, or quadratic function. a. a bacteria culture that doubles every 30 minutes

[ Ⓐ Linear Ⓑ Exponential Ⓒ Quadratic ]

b. the height of a roller coaster as it travels up and down a hill

[ Ⓐ Linear Ⓑ Exponential Ⓒ Quadratic ]

c. the total cost for each $2 ice cream cone purchased

[ Ⓐ Linear Ⓑ Exponential Ⓒ Quadratic ]

d. y = 2x² + 3x – 4

[ Ⓐ Linear Ⓑ Exponential Ⓒ Quadratic ]

e. y = 2x – 4

[ Ⓐ Linear Ⓑ Exponential Ⓒ Quadratic ]

x

[ Ⓐ Linear Ⓑ Exponential Ⓒ Quadratic ]

f. y = –5(2) 3.

Solve 2x² + 7x = 5 by using the Quadratic Formula. Round to the nearest tenth if necessary. Ⓐ x = –4, 0.5 Ⓑ x = –0.6, 4 Ⓒ x = –4.1, 0.6 Ⓓ x = –1, –2.5

4.

The discriminant of 2x² + 7x = 5 is [ Ⓐ 9 Ⓑ 26 Ⓒ 89 ].

5.

Sketch a graph of f(x) = x² – 8x + 7.

6.

BASKETBALL Dante makes a pass for Seth to dunk at their basketball game. The height y of the basketball after x seconds can be modeled by y = −16x² + 34x + 3, and the path of Seth’s jump can be modeled by y = 3x + 5. Solve a system of equations algebraically to calculate how long it will take Seth to catch the basketball. Round to the nearest tenth of a second. _______ seconds

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7.

Solve x2 + 14x + 31 = –5 by completing the square. Part A Complete the square. ( x + _______ )² = _______ Part B Solve the equation. Enter your solutions from least to greatest. Round to the nearest hundredth. x ≈ _______ or _______

8.

Match each dilation to its correct function as it relates to the parent function f(x) = x². a. j(x) =

( ) 1 x 2

2

_____

b. k(x) = 2x²

_____

c. h(x) = (2x)²

_____

d. g(x) =

1 2 x 2

_____

A vertical compression B horizontal stretch C vertical stretch D horizontal compression 9.

Given f(x) = –4x² + 2x – 2 and d(x) = 3x + 5, find (f · d)(x). (f · d)(x) = [ Ⓐ 12 Ⓑ –6 Ⓒ –12 ]x³ – [ Ⓐ 16 Ⓑ 20 Ⓒ 14 ]x² + [ Ⓐ 16 Ⓑ 4 Ⓒ 2 ]x – 10

Use the graph below to complete exercises 10 and 11.

10. Select all zeros of the quadratic function. Ⓐ (–3, 0) Ⓑ (0, 1) Ⓒ (0, –3) Ⓓ (3, 0) Ⓔ (1, 0) Ⓕ (0, 2)

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11. Identify the vertex and tell whether it is a minimum or a maximum. Ⓐ (–1, 3); minimum Ⓑ (–3, 0); minimum Ⓒ (–1, 3); maximum Ⓓ (3, –1); maximum 12. EGG DROP The physics class is holding an egg drop competition. The formula h = –16t² + h0 can be used to approximate the number of seconds t it will take for the eggs to reach height h from an initial height of h0 in feet. Find the time it takes an egg to reach the ground if it is dropped from an initial height of 40 feet. Round to the nearest hundredth if necessary. _________ seconds 13. Which transformations are displayed in the graph of g(x) = –(x + 3)² – 1 as it relates to the graph of the parent function? Select all that apply. Ⓐ Reflected over the x-axis Ⓑ Translated 3 units up Ⓒ Translated 3 units left Ⓓ Translated 1 unit up Ⓔ Translated 1 unit down Ⓕ Horizontally stretched 14. The graph of g(x) = (x – 2)² + 10 is a translation of the graph of the parent function ______ units right and ______ units up. 15. Which table shows quadratic behavior? Ⓐ

Ⓑ x 0 1 2 3

y 1 6 13 22

x 0 1 2 3

y 1 3 9 27

x 0 1 2 3

y 0 3 6 9

x 0 1 2 3

y –2 2 6 10

Ⓓ

Ⓒ

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16. Write a quadratic function for the graph. Round to the nearest hundredth if necessary.

f(x) = ______x² – ______ x + ______ 17. The vertex of the parabola for the graph of f(x) = 3(x – 2)² + 9 will be a [ Ⓐ minimum Ⓑ maximum ]. 18. Find the solution set of the system of equations graphed.

Ⓐ (–1, 0) and (3,0) Ⓑ (1, –3) Ⓒ (–1, 0) Ⓓ (–1, 0) and (2, –2) 19. SALES Feng studied a set of data showing the amount of greeting card sales around a holiday. He calculated the coefficient of determination, R², to find the best function model for the data. Which R² value shows the best model? Ⓐ 0.991 Ⓑ 0.919 Ⓒ 0.876 Ⓓ 0.819 20. Given f(x) = −2x² + 9x – 3 and g(x) = 12x + 5, find (g – f)(x). (g – f)(x) = ______x² + ______x + ______

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