Mr. Renz Unit 3 Algebra Review

Solve each equation by factoring.

100

49p² + 371p - 163 = 5

3/7, -8

200

9n² + 39n = -36

-4/3, -3

300

7r² + 84 = -49r

-4, -3

400

3v² + 7v = 40

8/3, -5

500

x² - 5x + 12x - 60 = 0

x = -12 or x = 5

Solve using square roots.

100

x² - 22 = 99

x = 11 or x = -11

200

4x² - 15 = -31

x = -4i or x = 4i

300

(4x + 1)² - 8 = 0

x = -1 + 2 square root of 2 / 4

or

x = -1 -2 square root of 2 / 4

400

y = (a - 2)² - 2

a = 4 + square root of 2/3

or

a = 4 - square root of 2/3

500

y = 3(x + 7)² - 24

x = -7 + 2 square root of 2

or

x = -7 - square root of 2

Solve each equation by completing the square.

100

x² + 10x + 25 = 9

x= 8 or x = 9

200

a² + 14a - 51 = 0

{3, -17}

300

x² − 12x + 11 = 0

{11, 1}

400

n² = 18n + 40

{20, −2}

500

x² − 10x + 26 = 8

{5 + square root 7, 5 square root − 7}

Solve each equation with the quadratic formula

100

m² − 5m − 14 = 0

{7, −2}

200

b² − 4b + 4 = 0

{2}

300

2x² − 3x − 5 = 0

{5/2 , −1}

400

9n² = 4 + 7n

{ 7 + square root of 193 / 18, 7 - square root of 193 / 18}

500

A softball player throws a ball in the outfield at an initial velocity of 80 feet/sec at a height of 6 feet. The catcher at home plate catches the ball at a height of 1 foot from the ground. How long was the ball in the air?

About 5.1 seconds

Imaginary

100

Add or Subtract the following:

(5 - 4i) + (-2 - 5i)           

3 - 9i

200

Add or Subtract the following:

(10 + 3i) - (17 + 8i)

-7 - 5i

300

Multiply the following:

(-3i)(5i)

15

400

Multiply the following:

(3 + 4i)(9 - 2i)

35 + 30i

500

Multiply the following:

(7 - 5i)²

24 - 70i