Free Printable Quadratics

1.

What are the zeros of the graph $y=x^2–7x–18?$

a)

x = -2, x = 9

b)

x = 3, x = 0

c)

x = 0, x = -18

d)

x = -3, x = -4

2.

The height (h) of a stone thrown straight up with a velocity of 24 m/sec is given by the relation h= -6t² + 24t. How long will it take for the stone to reach its maximum height? What is the maximum height?

a)

2 sec; 0 m

b)

2 sec; 24 m

c)

4 sec; 24 m

d)

4 sec; 0 m

3.

Which point is not on the graph represented by $y=x^2+3x-6?$

a)

(-6, 12)

b)

(2, 4)

c)

(-4, -2)

d)

(3, -6)

4.

Joel rewrites a quadratic equation by completing the square. The resulting equation is y = (x + 5)² – 2. He then draws the graph that models this equation. What is the vertex point of this quadratic?

a)

(5, -2)

b)

(-5, -2)

c)

(-2, 5)

d)

(-2, -5)

5.

In the function $f\left(x\right)=\left(x-2\right)^2+4$ , the minimum value occurs when x is

a)

-2

b)

2

c)

-4

d)

4

6.

Solve: $x(x–10)=24$

a)

x = -6, x = 6

b)

x = -12, x = 2

c)

x = -2, x = 12

d)

x = -6, x = 0, x = 6

7.

Identify the zeros of the function above.

a)

x = -2 and x = 1

b)

x = 0

c)

x = -2.1 and x = 0.5

d)

x = -2, x = 0, and x = 1

8.

Which equation has the same solution as $2x^2+x-3=0$ .

a)

(2x – 1)(x + 3) = 0

b)

(2x + 1)(x – 3) = 0

c)

(2x – 3)(x + 1) = 0

d)

(2x + 3)(x – 1) = 0

9.

Which function, f(x), has roots of 3 and –4?

a)

$f(x)=x^2+x-12$

b)

$f(x)=x^2-3x-4$

c)

$f(x)=x^2-x-12$

d)

$f(x)=x^2-4x+3$

10.

The square of a positive number decreased by 3 times the number is 28.

Find the number.

a)

-7

b)

-4

c)

7

d)

4

11.

Rewrite the following equation in vertex form:
$y=-2x^2+4x+8$

a)

$y=-2\left(x-1\right)^2+10$

b)

$y=-2\left(x-1\right)^2-10$

c)

$y=-2(x+1)^2+10$

d)

$y=-2\left(x+1\right)^2-10$

12.

What is the average rate of change for $f\left(x\right)=-x^2+4x+8$
over the interval [-1, 3]?

a)

-2

b)

2

c)

0

d)

$\frac{1}{2}$

13.

Which equation has the same solution as $x^2–6x–12=0$ ?

a)

$(x+3)^2=3$

b)

$(x–3)^2=3$

c)

$(x+3)^2=21$

d)

$(x–3)^2=21$

14.

If the quadratic formula is used to find the roots of the equation $x^2-6x-19=0$ , the correct roots are

a)

$3\pm2\sqrt{7}$

b)

$3\pm4\sqrt{14}$

c)

$-3\pm2\sqrt{7}$

d)

$-3\pm4\sqrt{14}$

15.

Find the average rate of change for the following table in the interval $-1\le x\le2$ .

a)

-3

b)

$-\frac{1}{3}$

c)

-9

d)

$-\frac{1}{9}$

16.

Solve, algebraically, for the value(s) of x: $4x^2-4x=24$

a)

x= 3, -2

b)

x= 4, -2 ,3

c)

x= -2, 3

d)

x= -3, 2

17.

Given the following graph of a quadratic function, write the equation in standard form.

a)

$x^2+4x-32$

b)

$x^2-4x-32$

c)

$-x^2-4x+32$

d)

$-x^2+4x+32$

18.

Write the function rule in vertex form.

a)

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

b)

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

c)

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

d)

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

19.

Solve the following equation and write the solution in simplest radical form. $3x^2-6x-11=0$

a)

$\frac{-3\pm\sqrt{42}}{3}$

b)

$\frac{3\pm\sqrt{42}}{3}$

c)

$\frac{3\pm2\sqrt{6}}{3}$

d)

$\frac{6\pm\sqrt{168}}{6}$

20.

An 8 inch by 10 inch mirror was placed in a frame and hung on the wall. The mirror and frame together cover an area of 130 square inches. How wide is the frame? Solve using an algebraic method. Round your answer to the nearest 10th of an inch.

a)

1.2 in

b)

18.2 in

c)

9.2 in

d)

8.4 in

21.

A rocket is launched from the ground with a velocity of 12 ft/sec and follows a parabolic path represented by the equation $y=-2x^2+12x$ .

How long does it take for the rocket to reach its maximum height? (algebraically)

a)

After 3 seconds

b)

After 2 seconds

c)

After 6 seconds

d)

After $\frac{1}{12}$ seconds

22.

A rocket is launched from the ground with a velocity of 12 ft/sec and follows a parabolic path represented by the equation $y=-2x^2+12$ .
What is the maximum height that the rocket reaches? (Algebraically)

a)

16 feet

b)

6 feet

c)

18 feet

d)

12 feet

23.

A rocket is launched from the ground with a velocity of 12 ft/sec and follows a parabolic path represented by the equation $y=-2x^2+12x$ .
How many seconds after the launch will the rocket hit the ground? (algebraically)

a)

After 3 seconds

b)

After 6 seconds

c)

After 2 seconds

d)

After 18 seconds

Quadratics

Total questions: 23

Worksheet time: 12mins

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