Unit 9 Review

Which function has a vertex on the y-axis?

• $f\left(x\right)=\left(x-2\right)^2$

• $f\left(x\right)=x\left(x+2\right)$

• $f\left(x\right)=\left(x-2\right)\left(x+2\right)$

• $f\left(x\right)=\left(x+1\right)\left(x-2\right)$

Answer explanation

Remember, if the vertex is on the y-axis, then the zeros, or x-intercepts, must be opposites.

Which translation maps the graph of the function f(x)=x² onto the function g(x) = x² - 6x + 6?

• left 3 units, down 3 units

• right 3 units, down 3 units

• left 6 units, down 1 unit

• right 6 units, down 1 unit

Answer explanation

In order to find the translation, you need to convert from standard form to vertex form.

What is the y-value of the vertex of the function f(x) = -(x-3)(x+11)?

• -8

• -4

• 33

• 49

Answer explanation

In order to find the vertex from factored form, find the axis of symmetry, then evaluate the function at that x-value.

The curve produced by the water coming from a fountain is sketched on the graph. Which function does the graph represent?

• $f\left(x\right)=\left(x-2\right)^2+3$

• $f\left(x\right)=-\left(x-2\right)^2+3$

• $f\left(x\right)=\left(x+2\right)^2+3$

• $f\left(x\right)=-\left(x+2\right)^2+3$

Answer explanation

The curve opens down so the leading coefficient must be negative.

Tags

CCSS.HSF-IF.C.7A

Which is the rate of change for the interval between 3 and 6 on the x-axis?

• -3

• -2

• 2

• 3

Answer explanation

The graph is increasing from 3 to 6 so the rate of change is positive. The y values increase by 6 while the x values increase by 3.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Which is f(6) for the quadratic function graphed?

• -2

• -0.5

• 1.5

• 4

Answer explanation

f(6) means to find the y-value when x = 6.

Tags

CCSS.HSF.IF.A.2

What is the missing value in the last step?

• 3

• 6

• 9

• 18

Answer explanation

The squared binomial comes from half of the linear term.

The function f(x) = x² is translated 7 units to the left and 3 units down to form the function g(x). Which represents g(x)?

• $g\left(x\right)=\left(x-7\right)^2-3$

• $g\left(x\right)=\left(x+7\right)^2-3$

• $g\left(x\right)=\left(x-3\right)^2-7$

• $g\left(x\right)=\left(x-3\right)^2+7$

Answer explanation

7 units to the left translated to x + 7 and 3 units down is -3

A boy throws a baseball across a field. The ball reaches its maximum height, 18 meters, after 1 second. After approximately 2.3 seconds, the ball lands on the ground. The ball’s motion can be modeled using the given function. What is the height of the ball 1.5 seconds after it is thrown?

 $f\left(x\right)=-10x^2+20x+8$  

• 11.7

• 13.8

• 15.5

• 17.5

Answer explanation

Evaluate for x = 1.5

Which equation, when graphed, has x-intercepts at (8, 0) and (−2, 0) and a y-intercept at (0, −48)?

• $f\left(x\right)=-3\left(x-8\right)\left(x+2\right)$

• $f\left(x\right)=-3\left(x+8\right)\left(x-2\right)$

• $f\left(x\right)=3\left(x-8\right)\left(x+2\right)$

• $f\left(x\right)=3\left(x+8\right)\left(x-2\right)$

Answer explanation

Convert the function from factored form into standard form by multiplying the factors. The value of "c" is the y-intercept.