Free Printable Quadratic Functions and Equations

1.

What are the x-intercepts of y = (x - 6)(x - 9)?

a)

6 and 9

b)

-6 and -9

c)

-6 and 9

d)

6 and -9

2.

What is the axis of symmetry of $f\left(x\right)=2\left(x+6\right)^2-3$ ?

a)

x = 2

b)

x = -3

c)

x = -6

d)

x = 6

3.

What is the quadratic function in vertex form for the parabola shown?

a)

$f\left(x\right)=-8\left(x-2\right)^2+1$

b)

$f\left(x\right)=-8\left(x-1\right)^2+2$

c)

$f\left(x\right)=8\left(x+1\right)^2+1$

d)

$f\left(x\right)=8\left(x-1\right)^2-2$

4.

What is the vertex of $y=7\left(x+5\right)^2+4$ ?

(a)

5.

Which graph represents the quadratic function $y=\frac{5}{7}\left(x-4\right)^2-7$ ?

a)

b)

c)

d)

6.

What are the domain and range of $y=7\left(x-1\right)^2-9$ ?

a)

Domain $\left\{x\parallel x\le-1,\ x\epsilon R\right\}$
Range $\left\{y\parallel y\epsilon R\right\}$

b)

Domain $\left\{x\parallel x\epsilon R\right\}$
Range $\left\{y\parallel y\ge-9,\ y\epsilon R\right\}$

c)

Domain $\left\{x\parallel x\ge7,\ x\epsilon R\right\}$
Range $\left\{y\parallel y\epsilon R\right\}$

d)

Domain $\left\{x\parallel x\epsilon R\right\}$
Range $\left\{y\parallel y\le-1,\ y\epsilon R\right\}$

7.

The vertex of a parabola is located at (-5, 6). If the parabola has a y-intercept of 231, which quadratic function represents the parabola?

a)

$f\left(x\right)=9\left(x-5\right)^2+6$

b)

$f\left(x\right)=9\left(x+5\right)^2+6$

c)

$f\left(x\right)=-9\left(x+5\right)^2+6$

d)

$f\left(x\right)=9\left(x-5\right)^2-6$

8.

What information can be determined from the quadratic function $f\left(x\right)=\frac{2}{3}\left(x+2\right)^2-9$ ?

a)

the vertex is at (–2, –9) and the graph opens upward

b)

the vertex is at (–9, –2) and the graph opens downward

c)

the vertex is at (–2, –9) and the graph opens downward

d)

the vertex is at (–9, –2) and the graph opens upward

9.

Which function is not quadratic?

a)

$f\left(x\right)=\left(6x+9\right)\left(\frac{1}{9}x-9\right)$

b)

$f\left(x\right)=x\left(x-9\right)\left(6x+8\right)$

c)

$f\left(x\right)=7x^2+8$

d)

$f\left(x\right)=6\left(x-9\right)^2$

10.

Identify the characteristics of this graph.

a)

vertex: (–2, –5), axis of symmetry: x = -2, y-intercept: 10.5, x-intercepts: –3 and –7, opens downward

b)

vertex: (–5, –2), axis of symmetry: x = -5, y-intercept: 10.5, x-intercepts: –3 and –7, opens upward

c)

vertex: (–2, –5), axis of symmetry: x = -2, y-intercept: 10.5, x-intercepts: –3 and –7, opens upward

d)

vertex: (–5, –2), axis of symmetry: x = -2, y-intercept: 10.5, x-intercepts: 3 and 7, opens downward

11.

What is $g\left(x\right)=\left(-2x+6\right)\left(4x-14\right)$ written in standard form?

a)

$g\left(x\right)=-8x^2+28x+8$

b)

$g\left(x\right)=-8x^2+52x-84$

c)

$g\left(x\right)=2x^2-8$

d)

$g\left(x\right)=-8x^2-84$

12.

What are the coordinates of the vertex of the quadratic function $y=4x^2+8x-2$ ?

(a)

13.

What is the function $y=2\left(x-4\right)^2-2$ written in standard form?

a)

$y=2x^2-8x+30$

b)

$y=2x^2-8x+34$

c)

$y=2x^2-16x+34$

d)

$y=2x^2-16x+30$

14.

What is the function $y=\left(x+2\right)^2$ written in standard form?

a)

$y=x^2+4x+4$

b)

$y=x^2-4x+4$

c)

$y=x^2-2^2$

d)

$y=x^2+4$

15.

Which graph represents the quadratic function with the following characteristics: x-intercepts at 8 and 10, maximum of 1

a)

b)

c)

d)

16.

If the points (-1, 4) and (2, 13) are on the graph of the quadratic function $f\left(x\right)=7x^2+bx+c$ , what are the values of b and c?

a)

b = -3 and c = -9

b)

b = -7 and c = -4

c)

b = 9 and c = 3

d)

b = -4 and c = -7

17.

The table shows the path of an extraterrestrial missile, where x is the horizontal distance, in metres, from the launch pad and h is the height, in metres, of the missile above the launch pad. What quadratic equation can be used to model the data set?

a)

$h\left(x\right)=-0.4x^2+2.5x+2$

b)

$h\left(x\right)=-0.4x^2+5x+4$

c)

$h\left(x\right)=-0.4x^2-5x+4$

d)

$h\left(x\right)=-0.4x^2+5x-4$

18.

What is the equation of the quadratic function $y=x^2+24x+29$ in vertex form?

a)

$y=\left(x+12\right)^2-173$

b)

$y=\left(x-12\right)^2-115$

c)

$y=\left(x-12\right)^2-173$

d)

$y=\left(x+12\right)^2-115$

19.

What is the equation of the quadratic function $y=x^2-26x+41$ in vertex form?

a)

$y=-\left(x+13\right)^2-210$

b)

$y=-\left(x-13\right)^2-210$

c)

$y=\left(x+13\right)^2-128$

d)

$y=\left(x-13\right)^2-128$

20.

Which quadratic function in standard form represents $y=3\left(x-1\right)^2-25$ ?

a)

$y=3x^2-3x-11$

b)

$y=3x^2-6x-22$

c)

$y=3x^2+6x-22$

d)

$y=3x^2-6x-11$

21.

State whether the function $y=4x^2-36x-43$ has a maximum or minimum value and identify the coordinates of the vertex.

a)

maximum at (4.5, -124)

b)

maximum at (-124, 4.5)

c)

minimum at (-124, 4.5)

d)

minimum at (4.5, -124)

22.

The vertex of the quadratic function $y=\left(-\frac{7}{9}\right)x^2-\left(\frac{1}{6}\right)x-\frac{1}{81}$ is

a)

$(-\frac{3}{28},-\frac{31}{9072})$

b)

$(-\frac{31}{9072},-\frac{3}{28})$

c)

$\left(\frac{31}{9072},-\frac{3}{28}\right)$

d)

$(\frac{3}{28},-\frac{31}{9072})$

23.

What is the vertex form of $y=\frac{1}{4}x^2+\frac{1}{16}x-\frac{1}{64}$ ?

a)

$y=\frac{1}{4}\left(x+\frac{1}{8}\right)^2+\frac{5}{256}$

b)

$y=\frac{1}{4}\left(x+\frac{5}{256}\right)^2-\frac{1}{8}$

c)

$y=\frac{1}{4}\left(x+\frac{5}{256}\right)^2+\frac{1}{8}$

d)

$y=\frac{1}{4}\left(x+\frac{1}{8}\right)^2-\frac{5}{256}$

24.

Convert $y=-2.5x^2-36.7x-5.9$ to vertex form. Round coefficients to two decimal places, if necessary.

a)

$y=-2.5\left(x+7.34\right)^2+128.79$

b)

$y=-2.5\left(x-7.34\right)^2+128.79$

c)

$y=-2.5\left(x-7.34\right)^2+47.98$

d)

$y=-2.5\left(x+7.34\right)^2+47.98$

25.

What is the axis of symmetry for the quadratic function $y=-\frac{1}{3}x^2-\frac{1}{2}x-1$ ?

a)

x = -1/48

b)

x = -117/4

c)

x = -13/16

d)

x = -3/4

26.

How many x-intercepts does the graph of the quadratic function $f\left(x\right)=-2.3x^2-6.9x-4.6$ have?

(a)

27.

What are the x-intercepts of the quadratic function graphed here?

(a)

28.

What are the x-intercepts of the quadratic function $f\left(x\right)=0.3\left(x-4.6\right)^2+9.0$ ?

a)

4.6

b)

There are none

c)

-2.2

d)

9.0

29.

What is the x-intercept of the quadratic function $f\left(x\right)=4.8\left(x-2\right)^2$ ?

(a)

30.

What are the roots of the quadratic function $y=0.5x^2+3.5x+6$ ?

(a)

31.

What are the roots of the quadratic function $y=-6.1x^2-97.6x-390.4$

(a)

32.

Factor $x^2-20x+75$ completely.

a)

(x - 5)(x + 15)

b)

(x + 5)(x + 15)

c)

(x + 5)(x - 15)

d)

(x - 5)(x - 15)

33.

Factor $-4x^2+68x-120$ completely.

a)

-4(x - 2)(x - 15)

b)

-4(x + 2)(x + 15)

c)

-4(x + 2)(x - 15)

d)

-4(x - 2)(x + 15)

34.

Solve $-8x^2+120x+432=0$

a)

x = 18 and x = -3

b)

x = -18 and x = 3

c)

x = 9/4 and x = -3/8

d)

x = -144 and x = 24

35.

Determine the roots of the quadratic equation $-5x^2+55x=50$

a)

x = -10 and x = -1

b)

x = -50 and x = -5

c)

x = 10 and x = 1

d)

x = 2 and x = 1/5

36.

Determine the roots of the quadratic equation $144x^2-324=0$

a)

x = 4/9 and x = -4/9

b)

x = 3/2 and x = -3/2

c)

x = 9/4 and x = -9/4

d)

x = 2/3 and x = -2/3

37.

Solve (x + 4)(x - 9) = 0

a)

x = 4 and x = -9

b)

x = 4 and x = 9

c)

x = -4 and x = 9

d)

x = -4 and x = -9

38.

If the area of the rectangle is 72 cm² , what is the value of x, to the nearest tenth of a centimetre?

(a)

39.

The value of k that makes the expression $x^2+72x+k$ a perfect square trinomial is

(a)

40.

The vertex form of $4x^2+16x+11=0$ is

a)

$4\left(x+5\right)^2-2=0$

b)

$4\left(x-2\right)^2+5=0$

c)

$4\left(x+2\right)^2-5=0$

d)

$4\left(x-2\right)^2-5=0$

41.

Which is the vertex form of $2x^2-12x-10=0$ ?

a)

$2\left(x+3\right)^2-28=0$

b)

$2\left(x-28\right)^2-3=0$

c)

$2\left(x+3\right)^2+28=0$

d)

$2\left(x-3\right)^2-28=0$

42.

Solve $\left(x+1\right)^2=43$

a)

$1\pm\sqrt{43}$

b)

$-1\pm\sqrt{43}$

c)

$2\sqrt{11}$

d)

$\sqrt{42}$

43.

The roots, to the nearest hundredth, of $y=-\frac{1}{2}x^2-2x+\frac{7}{10}$ are

(a)

44.

The roots, to the nearest hundredth, of $y=7.2x^2-33.1x+18.3$ are

a)

7.91 and 1.29

b)

1.98 and 0.32

c)

3.95 and 0.64

d)

–3.95 and –0.64

45.

A rectangle with an area of 2504 cm² is x centimetres wide and (x + 8) centimetres long. To the nearest tenth of a centimetre, the width and length are

a)

50.0 cm and 50.0 cm

b)

–46.2 cm and –54.2 cm

c)

46.2 cm and 54.2 cm

d)

–14.0 cm and 114.0 cm

46.

When Alex rides his dirt bike off a ramp, his path can be modelled by $h\left(d\right)=-3.9d^2+13.1d+8.7$ , where d is the horizontal distance from the ramp and h is the height, both in metres. How far away from the ramp does he land, to the nearest tenth of a metre?

(a)

47.

The x-intercepts, to the nearest hundredth, of $y=-33.8x^2+6.8x+13.4$ are

a)

–0.27 and 0.37

b)

–0.54 and 0.74

c)

–1.07 and 1.48

d)

–0.64 and 0.64

48.

The number of real roots for the equation $y=-30.6x^2+30.7x-39.8$ is

(a)

49.

For a science experiment, a projectile is launched. Its path is given by $h\left(d\right)=-4.0d^2+61.3d+20.9$ , where h is the height of the projectile above the ground and d is the horizontal distance of the projectile from the launch pad, both in metres. How far away from the launch pad is the projectile when it begins to fall, to the nearest tenth of a metre?

(a)

50.

The table shows the coordinates of the curve of a parabolic arch at the entrance to a park, where x is the horizontal distance from one side of the arch and h is the height of the arch above ground, both in metres. The quadratic equation that models the data is

a)

$y=4x^2+8x+6$

b)

$y=4x^2-8x+6$

c)

$y=-4x^2-8x-6$

d)

$y=-4x^2+8x+6$

Quadratic Functions and Equations

Total questions: 50

Worksheet time: 2hrs 38mins

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