Free Printable Graphing Quadratic Functions

1.

Which graph matches the function $r\left(x\right)=2\left(x+3\right)^2-5$ ?

a)

b)

c)

d)

2.

What are the transformations of the function $r\left(x\right)=2\left(x+3\right)^2-5$ compared to the quadratic parent function $f\left(x\right)=x^2$ ?

a)

vertical shrink by $\frac{1}{2}$ , left 3, down 5.

b)

vertical stretch by 2, right 3, down 5.

c)

vertical reflection, left 3, down 5.

d)

vertical stretch by 2, left 3, down 5

3.

Which graph matches the function $h\left(x\right)=-\frac{1}{3}x^2$ ?

a)

b)

c)

d)

4.

What are the transformations of the function $h\left(x\right)=-\frac{1}{3}x^2$ compared to the quadratic parent function $f\left(x\right)=x^2$ ?

a)

vertical reflection, vertical stretch of 3

b)

vertical reflection, vertical shrink of $\frac{1}{3}$

c)

horizontal reflection, vertical shrink of $\frac{1}{3}$

d)

vertical shrink of $\frac{1}{3}$

5.

Which of the following equations satisfies the given criteria: passing through (0, 0), (2, 2), (4, 0)?

a)

y=-\frac{1}{2}x^2+2x

b)

$y=\frac{1}{2}x^2+2x$

c)

$y=-\frac{1}{6}x^2+\frac{2}{3}x$

d)

$y=\frac{1}{6}x^2+\frac{2}{3}x$

6.

Which of the following equations satisfies the given criteria: x-intercepts : -5, 8?

a)

$y=x^2+13x+40$

b)

$y=x^2+3x-40$

c)

$y=x^2-3x-40$

d)

$y=x^2-13x+40$

7.

State the zeros of the function $g\left(x\right)=x^3-16x$ .

a)

x=16, x=0

b)

x=-4, x=4

c)

x=-4, x=0, x=4

d)

no real solutions

8.

State the zeros of the function $f\left(x\right)=3x^2-6x-45$ .

a)

x=-3, x=3, x=5

b)

x=-3, x=5

c)

x=-5, x=3

d)

no real solutions

9.

Find the domain and range

a)

D: All Real Numbers, R: $\left\{-4\ge y\right\}$

b)

D: $\left\{-6\le x\le0\right\}$ , R: $\left\{-4\le y\le5\right\}$

c)

D: All Real Numbers, R: $\left\{-3\le y\right\}$

d)

D: All Real Numbers, R: $\left\{-4\le y\right\}$

10.

State the zeros.

a)

(-5, 0), (-3, -4)

b)

(-5, 0), (-1, 0)

c)

no real solutions

d)

(-1, 0), (-3, -4)

11.

Identify the equation of the parabola in vertex form.

a)

$y=-\frac{1}{2}x^2-2x-\frac{3}{2}$

b)

$y=\left(x-3\right)^2-4$

c)

$y=2\left(x+3\right)^2-4$

d)

$y=\left(x+3\right)^2-4$

12.

What are the transformations of the graph compared to the graph of $f\left(x\right)=x^2$ ?

a)

Left 3, down 4

b)

left 4, down 3

c)

right 3, down 4

d)

vertical stretch by 2, left 3, down 4

13.

Which of the following transformations would translate the function $f\left(x\right)=x^2$ 2 units to the right?

a)

$h\left(x\right)=f\left(x\right)+2$

b)

$h\left(x\right)=f\left(x+2\right)$

c)

$h\left(x\right)=f\left(x\right)-2$

d)

$h\left(x\right)=f\left(x-2\right)$

14.

The height (in feet) of an eagle diving to catch a field mouse is represented by $h\left(t\right)=2\left(t-5\right)^2+1$ , where t is the number of seconds after beginning the dive. After how many seconds does the eagle reach the mouse?

a)

1 second

b)

3 seconds

c)

5 seconds

d)

9 seconds

15.

The height (in feet) of an eagle diving to catch a field mouse is represented by $h\left(t\right)=2\left(t-5\right)^2+1$ , where t is the number of seconds after beginning the dive. After diving toward the mouse, when will the eagle soar up to 33 feet in the air?

a)

1 second

b)

3 seconds

c)

5 seconds

d)

9 seconds

16.

State the vertex and axis of symmetry for the following function $f\left(x\right)=-\frac{1}{2}\left(x-3\right)^2$ .

a)

(-3, 0), x=-3

b)

(3, 0) x= $-\frac{1}{2}$

c)

(3, 0), x=3

d)

(3, 0), y=0

17.

State the vertex and the axis of symmetry of the following function $g\left(x\right)=4x^2-48x+7$ .

a)

(0, 7), x=0

b)

(6, -137), y=-137

c)

(6,-137), x=6

d)

(6, -137), y=6

18.

During a baseball game a batter pops the ball up in the air. The height (in feet) of the baseball is modeled by the function $h\left(x\right)=-2x^2+21x-7$ , where x is the distance the ball has traveled horizontally. What is the maximum height the ball reaches?

a)

5.25 feet

b)

10.155 feet

c)

.345 feet

d)

48.125 feet

19.

During a baseball game a batter pops the ball up in the air. The height (in feet) of the baseball is modeled by the function $h\left(x\right)=-2x^2+21x-7$ , where x is the distance the ball has traveled horizontally. The catcher gets in position to make the out, how far does the catcher move horizontally from where the ball was hit to be directly under it at its maximum height?

a)

5.25 feet

b)

10.155 feet

c)

.345 feet

d)

48.125 feet

20.

The table shows the distance d (in miles) that you are away from home after driving t minutes away from the football game that you attended that evening. State whether the data can be modeled by a linear, an exponential or a quadratic function.

a)

Linear, $y=-\frac{1}{2}x+25$

b)

Exponential, $y=25\left(\frac{1}{2}\right)^x$

c)

Quadratic, $y=x^2-\frac{1}{2}x+25$

21.

Determine the type of function the ordered pairs represent. (-3, 10), (-2, 5), (-1, 2), (0, 1), (1, 2)

a)

linear

b)

exponential

c)

quadratic

22.

Determine the type of function the ordered pairs represent. (-1, $\frac{1}{2}$ ), (0, 1), (1, 2), (-2, $\frac{1}{4}$ ), (2, 4)

a)

linear

b)

exponential

c)

quadratic

23.

Determine the type of function the ordered pairs represent. (-4, 7), (1, 2), (-3, 6), (-2, 5), (0, 3)

a)

linear

b)

exponential

c)

quadratic

24.

Determine the function which models the data.

a)

$y=2x$

b)

$y=2x^2$

c)

$y=2\left(1\right)^x$

d)

$y=2^x$

25.

Determine the function that models the data.

a)

$y=2x-3$

b)

$y=x^2-2x+3$

c)

$y=2\left(3\right)^x$

d)

$y=-2x+3$

Graphing Quadratic Functions

Total questions: 25

Worksheet time: 13mins

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