Free Printable Quadratic Formula Practice

1.

In the equation
y = x² +5x +7, match each leading coefficient with its correct letter

a)

a=0, b=5, c=7

b)

a=1, b=5, c=7

c)

a=7, b=5, c=1

2.

The discriminant is

a)

aX² + bX + c

b)

b - 4ac

c)

b² - 4ac

d)

b² + 4ac

3.

If the discriminant equals zero, the quadratic has how many solutions?

a)

2 real

b)

2 complex

c)

1 real

d)

1 complex

e)

0 real

4.

If the discriminant equals +35, the quadratic has how many solutions?

a)

2 real

b)

2 complex

c)

1 real

d)

1 complex

e)

0 real

5.

If the discriminant equals -72, the quadratic has how many solutions?

a)

2 real

b)

2 complex

c)

1 real

d)

1 complex

e)

0 real

6.

____________
For the function above, is the discriminant positive, negative, or zero?

a)

Positive

b)

Negative

c)

Zero

d)

Not Sure

7.

Which graph has a discriminant > 0?

a)

None of them

b)

Red

c)

Blue

d)

Green

8.

____________
For the function above, is the discriminant positive, negative, or zero?

a)

Positive

b)

Negative

c)

Zero

d)

Not Sure

9.

Solve by the Quadratic Formula:

$-12q^2+3q+7=0$

a)

$\frac{-3\pm\sqrt{345}}{24}$

b)

$\frac{3\pm\sqrt{345}}{-24}$

c)

$\frac{3\pm\sqrt{345}}{24}$

d)

$\frac{3\pm i\sqrt{39}}{24}$

10.

ax²+bx+c=0 is the standard form of a quadratic equation.

a)

True

b)

False

11.

In the equation ax²+bx+c=0, the x² term always corresponds with

a)

a

b)

b

c)

c

12.

In the equation ax²+bx+c=0, the c term always the

a)

x²term

b)

x term

c)

constant

13.

In the equation ax²+bx+c=0, the x term always corresponds with

a)

a

b)

b

c)

c

14.

Determine the values of
a, b, and c for
the quadratic equation:
4x² – 8x = 3
*remember right side should =0

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

15.

In the equation x²+4=0, match each leading coefficient with its correct letter.

a)

a=0 b=4 c=0

b)

a=1 b=4 c=0

c)

a=1 b=0 c=4

16.

Solve the quadratic equation.
2p² - 2p - 55 = 5

a)

A . {3.28, -2.28}

b)

B . {2.5, -1.78}

c)

C . {6, -5}

d)

D . {-1, 4}

17.

What should you do first in solving this equation?
x² + 6x - 13 = 3

a)

Get factored form

b)

Write down: a=1, b=6, c=-13

c)

Make it equal 0 by subtracting 3 on each side

d)

Type it all in a calculator.

18.

For the function below, is the discriminant positive, negative, or zero?

___________

y = x² + 4x + 4

a)

Positive

b)

Negative

c)

Zero

d)

Not Sure

19.

What is the discriminant of -2x² − x − 1 = 0

a)

76

b)

-7

c)

9

d)

none of these

20.

What is the discriminant of 6x² − 2x − 3 = 0

a)

76

b)

29

c)

68

d)

none of these

21.

Determine the value of the discriminant and name the nature of the roots for the following:
x² + 7x + 13
Remember: b² - 4ac

a)

400, 2 real root

b)

0, 1 real root with a multiplicity of 2

c)

-400, 2 imaginary roots

d)

-3, 2 imaginary roots

22.

What is the discriminant of this equation?

3x² + 8x = 0

a)

64

b)

52

c)

9

d)

0

23.

1 What does the discriminant tell us?

a)

The maximum or minimum

b)

The y-intercept

c)

The number and type of solutions

d)

The axis of symmetry

24.

What is the discriminant of 6x² − 2x − 3 = 0

a)

76

b)

29

c)

68

d)

none of these

25.

Use the graph to determine the solutions.

a)

-1 and -3

b)

1 and -3

c)

1 and 3

d)

-1 and 3

26.

Does y = -4x² have a maximum or minimum value?

a)

maximum

b)

minimum

27.

Does this graph in the back have maximum or minimum value?

a)

maximum

b)

minimum

c)

neither

d)

both

28.

The solutions of a quadratic equation are known as the _____.

a)

Vertices

b)

Roots

c)

Squares

d)

Formulas

29.

What is the axis of symmetry?

a)

the slope of the graph

b)

the dividing line for a parabola

c)

a way to spin my pencil

d)

the x-axis

30.

Determine the values of
a, b, and c for
the quadratic equation:
4x² – 8x = 3

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

31.

Which of the following is Standard Form?

a)

$y=ax^2+bx+c$

b)

$y=a\left(x-p\right)\left(x-q\right)$

c)

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

32.

Which of the following is Vertex Form?

a)

$y=ax^2+bx+c$

b)

$y=a\left(x-p\right)\left(x-q\right)$

c)

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

33.

What is an equation of a parabola with the vertex of $\left(-2,-4\right)$ ?

a)

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

b)

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

c)

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

d)

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

34.

What is an equation of a parabola with the vertex of $\left(4,9\right)$ ?

a)

$y=-\frac{4}{5}\left(x+4\right)^2-9$

b)

$y=\frac{3}{4}\left(x-4\right)^2+9$

c)

$y=-\frac{5}{2}\left(x-4\right)^2-9$

d)

$y=\left(x+4\right)^2+9$

35.

What is an equation of a parabola with the vertex of $\left(3,-4\right)$ ?

a)

$y=-\frac{1}{2}\left(x+3\right)^2-4$

b)

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

c)

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

d)

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

36.

$y=8\left(x-2\right)\left(x+3\right)$ What are the zeros (x-intercepts) of the equation

a)

$\left(2,0\right)\ and\ \left(3,0\right)$

b)

$\left(-2,0\right)\ and\ \left(3,0\right)$

c)

$\left(2,0\right)\ and\ \left(-3,0\right)$

d)

$\left(-2,0\right)\ and\ \left(-3,0\right)$

37.

$y=\frac{1}{4}\left(x+5\right)\left(x-6\right)$ What are the zeros (x-intercepts) of the equation

a)

$\left(5,0\right)\ and\ \left(6,0\right)$

b)

$\left(-5,0\right)\ and\ \left(6,0\right)$

c)

$\left(5,0\right)\ and\ \left(-6,0\right)$

d)

$\left(-5,0\right)\ and\ \left(-6,0\right)$

38.

How many solutions are there?

a)

0

b)

1

c)

2

d)

Cannot be determined

39.

What is the axis of symmetry?

a)

x= 4

b)

x=3

c)

x=-3

d)

Cannot be determined

40.

What is the axis of symmetry?

a)

x=0

b)

x=1

c)

x=2

d)

x=3

Quadratic Formula Practice

Total questions: 40

Worksheet time: 58mins

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