Module 9 Quadratics Review_NF

Lesson 9.01

If the equation for the axis of symmetry of a parabola is x = 0, which of the following statements must be true?

• b = 0 for the graphed quadratic function, f(x) = ax² + bx + c.

• c = 0 for the graphed quadratic function, f(x) = ax² + bx + c.

• The parabola opens up.

• The parabola opens down.

Lesson 9.01

A football is kicked toward the goal. The height of the ball is modeled by the function

h(t) = −16t² + 64t, where t equals the time in seconds and h(t) represents the height of the ball at time t seconds. What is the axis of symmetry, and what does it represent?

• t = 2; it takes 2 seconds to reach the maximum height and 2 more seconds to fall back to the ground

• t = 2; it takes 2 seconds to reach the maximum height and 4 more seconds to fall back to the ground

• t = 4; it takes 2 seconds to reach the maximum height and 4 more seconds to fall back to the ground

• t = 4; it takes 2 seconds to reach the maximum height and 8 more seconds to fall back to the ground

Lesson 9.01

Identify the range of the graph of

f(x) = 2x² + 8x − 9.

• y ≤ -2

• y ≥ -2

• y ≤ 15

• y ≥ 15

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

Lesson 9.01

The distance traveled, in feet, of a ball dropped from a tall building is modeled by the equation d(t) = 16t² where d equals the distance traveled at time t seconds and t equals the time in seconds. What does the average rate of change of d(t) from t = 2 to t = 5 represent?

• The ball travels an average distance of 48 feet from 2 seconds to 5 seconds.

• The ball travels an average distance of 112 feet from 2 seconds to 5 seconds.

• The ball falls down with an average speed of 48 feet per second from 2 seconds to 5 seconds.

• The ball falls down with an average speed of 112 feet per second from 2 seconds to 5 seconds.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Lesson 9.01

If f(x) = x², in which direction and by how many units should f(x) be shifted to obtain g(x) = x² + 8x + 16?

• Left by 4 units

• Right by 4 units

• Left by 8 units

• Right by 8 units

Lesson 9.02

In the function f(x) = 4(x² − 6x + ____ ) + 20, fill in the blank to complete the square.

• -3

• 3

• 9

• 36

Tags

CCSS.HSA-REI.B.4B

Lesson 9.02

The cost to produce a product is modeled by the function f(x) = 5x² − 70x + 258, where x is the number of products produced. Complete the square to determine the minimum cost of producing this product.

• f(x) = 5(x − 7)² + 13; The minimum cost to produce the product is $7.

• f(x) = 5(x − 7)² + 13; The minimum cost to produce the product is $13.

• f(x) = 5(x − 7)² + 258; The minimum cost to produce the product is $7.

• f(x) = 5(x − 7)² + 258; The minimum cost to produce the product is $258.

Lesson 9.02
Solve  $3x^2+18x+15=0$  by completing the square.

• x = -5, -1

• x = -11, -7

•  $x=-3\pm\sqrt{2}$  

•  $x=-9\pm\sqrt{76}$  

Tags

CCSS.HSA-REI.B.4B

Lesson 9.04

How can you tell when a quadratic equation has no real solutions?

• When the radicand (the value inside the square root) equals zero

• When the radicand (the value inside the square root) is negative

• When the radicand (the value inside the square root) is not a perfect square

• When the b-value in the quadratic equation is greater than the value in the radicand (the value inside the square root)

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7

Lesson 9.04

Use the quadratic formula to find the exact solutions of x² = 4 − 7x.

• $x=\frac{7\pm\sqrt{33}}{2}$

• $x=\frac{7\pm\sqrt{65}}{2}$

• $x=\frac{-7\pm\sqrt{33}}{2}$

• $x=\frac{-7\pm\sqrt{65}}{2}$

Tags

CCSS.HSA-REI.B.4B