Algebra Final Review(Quadratics)

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

Solve using square roots.

100

x² + 10x + 25 = 9

x= 8 or x = 9

200

(4x + 1)² - 8 = 0

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

or

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

300

y = (a - 2)² - 2

a = 4 + square root of 2/3

or

a = 4 - square root of 2/3

400

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

a² + 14a - 51 = 0

{3, -17}

200

x² − 12x + 11 = 0

{11, 1}

300

n² = 18n + 40

{20, −2}

400

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}

Converting forms

100

Convert from vertex form to standard form and factored form.              

y = −x² − 14x − 59

y = −(x + 7)² − 10

200

Convert from factored form to standard form and vertex form.

(x + 5)(x + 4) = =

y = (x + 9/2⁾² − 1/4

300

Convert from standard form to factored and vertex form.

y = x² − 6x + 5

y = (x − 3)² − 4

400

Convert from standard form to factored and vertex form.

 x² - 6x - 7 = 0

y = (x - 3)² - 16