Free Printable quadratic formula & square root property

Worksheets

quadratic formula & square root property

Total questions: 23

Worksheet time: 1hrs 1mins

Name

Class

Date

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

No Real Solution

The discriminant is

aX² + bX + c

b - 4ac

b² - 4ac

b² + 4ac

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

Positive

Negative

Zero

Not Sure

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

Positive

Negative

Zero

Not Sure

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

___________

y = x² + 4x + 4

Positive

Negative

Zero

Not Sure

If the discriminant is positive, then the solution will be

one real solution

two real solutions

no real solutions

one imaginary solution

4 Determine the value of the discriminant and name the nature of the solution for the following:

x² + 2x - 63

Remember: b² - 4ac

256 - 2 reals - Rational

√(-256 - 2 imaginary solutions

√(137) - 2 reals - Irrational

123 - 2 reals - Rational

If the discriminant is equal to 10, how many solutions are there?

2 Real, Irrational Solutions

1 Real Solution

2 Real Rational Solutions

No Real Solutions

If the discriminant is equal to 49, how many solutions are there?

No Real Solutions

1 Real Solution

2 Real, Rational Solutions

2 Real, Irrational Solutions

10.

A function has a discriminant of -3.
______________
How many x-intercepts does it have?

11.

True or false:
The solution, root, x-intercept, and zero of a problem are all the same thing

True

False, because the solution and root are the same but the x-intercept and zero are different

False, because the x-intercept and root are the same but the zero and solution are different

False, they are all different

12.

What does the discriminant tell us?

The maximum or minimum

The y-intercept

The number and type of solutions. (x-intercepts)

The axis of symmetry

13.

Solve by taking square roots.

2x² - 8 =100

x = ±√54

x = ±3√6

x = ± 9√6

x = ±2√27

14.

Solve using square roots.
k² - 6 = 43

k = √37

k = 37 or - 37

k = 7, k = -7

no solution

15.

When do you use the plus or minus symbol?
±

After taking the square root of both sides

After adding the square to both sides

After taking half of b

After setting the equation equal to zero

16.

$12-9x^2=38$

$\sqrt{-\frac{26}{9}}$

$\pm i\sqrt{\frac{26}{9}}$

$\pm\frac{i\sqrt{26}}{9}$

$\pm\frac{i\sqrt{26}}{3}$

17.

$5x^2+35=0$

$\pm\sqrt{-7}$

$\pm\sqrt{-35}$

$\pm i\sqrt{7}$

$\pm i\sqrt{35}$

18.

Determine the values of

a, b, and c for

the quadratic equation:

4x² – 8x = 3

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

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

a = 4, b = 8, c = 3

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

19.

Which graph has a discriminant = 0?

None of them

Red

Blue

Green

20.

A function has a discriminant of 0.

How many x-intercepts does it have?

21.

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

Get factored form

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

Make it equal 0 by subtracting 3 on each side

Type it all in a calculator.

22.

What is this formula?

This is the speed of light formula.

This is the quadratic formula.

This is the zero product property.

This is scary.

23.

Use the quadratic formula to solve 2x² + 2x - 12?

-2, 3

2, 3

2, -3

-2, -3

Reset

quadratic formula & square root property

Total questions: 23

Worksheet time: 1hrs 1mins

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