Free Printable Solving Quadratic Equations

1.

Which is the standard form for a quadratic equation?

a)

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

b)

$ax^2+bx+c=0$

c)

$y=a\left(x-h\right)^2+k$

d)

$a^2+b^2=c^2$

2.

Which is in the proper factored form to use the Zero Product Property ?

a)

$x^2-x=12$

b)

$x\left(x-1\right)=12$

c)

$\left(x-4\right)\left(x+3\right)=1$

d)

$\left(x-4\right)\left(x+3\right)=0$

3.

Given this graph is the function of

y=x^2-2x-8

, what is the solution to

x^2=2x+8

?

a)

(1, 9)

b)

x = {-2, 4}

c)

(0, 8)

d)

x = {5, 2}

4.

$7x^2=6x-1$

Given this quadratic equation, what could be the values a, b, and c to use in the quadratic formula?

a)

$a\ =\ 7,\ b\ =\ -6,\ c\ =\ 1$

b)

$a\ =\ 1,\ b\ =\ 6,\ c\ =\ -7$

c)

$a\ =\ -7,\ b\ =\ 6,\ c\ =\ 1$

d)

$a\ =\ 6,\ b\ =\ 7,\ c\ =\ 1$

5.

$x^2+12x$

What value completes the square?

a)

3

b)

6

c)

12

d)

36

6.

$x^2-7x=0$

Solve by the method of your choice.

a)

x = 7 only

b)

x = 0 only

c)

x = 0 and 7

d)

There is no real answer for this equation.

7.

$3x^2-10x+1=0$

Solve by the method of your choice.

a)

$x=\frac{-10\pm\sqrt{88}}{6}$

b)

$x=\frac{-5\pm2\sqrt{22}}{3}$

c)

$x=\frac{10\pm\sqrt{112}}{6}$

d)

$x=\frac{5\pm\sqrt{22}}{3}$

8.

$2x^2=8x+3$

2x^2-8x-3=0

x=\frac{8\pm\sqrt{64-4\left(2\right)\left(-3\right)}}{4}

x=\frac{8\pm\sqrt{40}}{4}

x=\frac{8\pm2\sqrt{10}}{4}

x=\frac{4\pm\sqrt{10}}{2}

Suzanne solved the equation using this process.

Did she make a mistake?

If yes, at which line did she make her first mistake?

(There are 5 steps in her process)

a)

Suzanne made no errors.

b)

Step 2

c)

Step 3

d)

Step 4

e)

Step 5

9.

What is the color of the graph that has exactly one real zero?

a)

black

b)

green

c)

purple

d)

red

e)

None of these graphs has exactly one zero.

10.

What is the color of the graph that has no real zeros?

a)

black

b)

green

c)

purple

d)

red

e)

None of these graphs have no real zeros

11.

How many real solutions can a quadratic equation of the form shown have?
Check all that apply.

ax^2+bx+c=0

a)

0

b)

1

c)

2

d)

3

e)

infinitely many

12.

When using factoring to solve a quadratic equation, what must be true?

a)

The equation must be set equal to 1.

b)

The equation must be set equal to 10.

c)

The equation must be set equal to 0.

d)

It is not necessary to set the equation equal to anything.

13.

What is the correct simplification to

\sqrt{x^2}

? Check all that apply.

a)

1

b)

x

c)

| x |

d)

$\pm$ x

14.

What is/are the solution(s) to

3x^2-1=74

?

a)

x = 5 only

b)

x = -5 only

c)

x = 5 and -5

d)

There are no real solutions

Solving Quadratic Equations

Total questions: 14

Worksheet time: 10mins

Similar Resources on Wayground