Free Printable PRACTICE- SQUARE ROOT METHOD & QUADRATIC FORMULA

1.

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

a)

True

b)

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

c)

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

d)

False, they are all different

2.

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

3.

In the equation

y = x² +5x +7, match each 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

d)

a=2, b=1, c=5

4.

Which of the following expressions represents the discriminant?

a)

ax² + bx + c

b)

b - 4ac

c)

b² - 4ac

d)

b² + 4ac

5.

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.

6.

Use quadratic formula to solve: $8x^2-4x-18=0$

a)

$\left\{\frac{1\pm\sqrt{37}}{4}\right\}$

b)

$\left\{8,4,18\right\}$

c)

$\left\{\frac{38}{4},-\frac{38}{4}\right\}$

d)

$i\sqrt{37}$

7.

$x^2-4x-7=0$
Which example below uses the quadratic formula correctly?

a)

$\frac{-\left(4\right)\pm\sqrt{\left(-4\right)^2-4\left(1\right)\left(-7\right)}}{2\left(1\right)}$

b)

$\frac{-\left(-4\right)\pm\sqrt{\left(-4\right)^2-4\left(1\right)\left(-7\right)}}{2\left(1\right)}$

c)

$\frac{-\left(-4\right)\pm\sqrt{\left(-4\right)^2-4\left(1\right)\left(7\right)}}{2\left(1\right)}$

8.

Solve using the quadratic formula:

$x^2-7x+1=0$

a)

$x=\frac{-7+3\sqrt{5}}{2}$ or $x=\frac{-7-3\sqrt{5}}{2}$

b)

$x=\frac{7+3\sqrt{5}}{2}$ or $x=\frac{7-3\sqrt{5}}{2}$

c)

$\frac{7-\sqrt{53}}{2}$ $x=\frac{7+\sqrt{53}}{2}$ or

d)

No Solution, because there is a negative under the square root.

9.

Solve Using the Quadratic Formula
x² + 4x - 40 = -8

a)

-10 & -4

b)

-4 & 10

c)

-8 & 4

d)

8 & -4

10.

7x² + 1 = 8

a)

± 1

b)

± 7

c)

± √7

d)

± 8

11.

Solve by taking square roots:
5b² - 4 = 41

a)

b = 9, b = -9

b)

b = 3, b = -3

c)

b = 8, b = -8

d)

no solution

12.

Solve using square roots.

a)

± 1/4

b)

± 9/36

c)

± 1/2

d)

No real solution

13.

x² + 4 = 68

a)

± 8

b)

± √8

c)

8

d)

± 64

14.

-5x² = -50

a)

± 5

b)

± 10

c)

± √10

d)

-10

15.

x² = 16

a)

± 4

b)

± 8

c)

4

d)

8

16.

If your discriminant is $d=81$ , state the number and type of roots your quadratic has.

a)

Two Real, Rational Roots

b)

Two Real, Irrational Roots

c)

One Real, Rational Root

d)

Two Imaginary Roots

17.

If your discriminant is $d=0$ , state the number and type of roots your quadratic has.

a)

Two Real, Rational Roots

b)

Two Real, Irrational Roots

c)

One Real, Rational Root

d)

Two Imaginary Roots

18.

Find the discriminant: $-4x^2+7x-1=0$

a)

$d=0$

b)

$d=-65$

c)

$d=113$

d)

$d=33$

19.

Find the discriminant AND state the number and types of roots: $10x=-5x^2-4$

a)

$d=20$ ; Two Real, Rational Roots

b)

$d=0$ ; Two Imaginary Roots

c)

$d=20$ ; Two Real, Irrational Roots

d)

$d=-64$ ; Two Imaginary Roots

20.

$m^2-5m-14=0$

a)

x = 7 and -2

b)

x = 7 and 2

c)

x = -7 and -2

d)

x = -7 and 2

PRACTICE- SQUARE ROOT METHOD & QUADRATIC FORMULA

Total questions: 20

Worksheet time: 2hrs 40mins

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