Quadratic Equations (Mixed Review)

Linear/Quadratic Systems

100

Solve by graphing. How many solutions does the following system have?

y = x² - 2x - 3

y = -5

No solution

200

Solve by graphing. How many solutions does the following system have?

y = -x² + 2x + 7

y = -2x + 2

2 solutions

300

Solve using substitution. State the solutions.

y = x² + 4x + 5

y = 2x + 3

(-4, -5) and (2, 7)

400

Solve using substitution. State the solutions.

y = x² - 6x + 5

2x + y = 5

(0,5) and (4, -3)

Find the Zeros by Factoring

100

p² + -2p - 15 = 0

x = {5, -3}

200

n² + 12n + 36 = 0

x = {-6)

300

7r² + 49r + 84 = 0

7(r^2 + 7r + 12) = 0

x = {-4, -3}

400

3v² + 12v = 15

3(v^2 + 4v - 5) = 0 

x = {-5, 1}

Solve Using Square Roots

100

4x² + 25 = 125

x= 5 or x = -5

200

(4x + 1)² - 16 = 0

x = 3/4 or x = -5/4

300

34 = (a - 2)² - 2

a = 8 or a = -4

400

0 = 3(x + 7)² - 24

x = -7 + 2 square root of 2

or

x = -7 - 2 square root of 2

Solve Using 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}

Quadratic Transformations

100

Dylan sketches a parabola with a vertex at the origin that opens downward. What is the equation of Dylan's function?

y = -x^2

200

Describe the transformation.

y = 1/6(x-3)² + 1

Vertically compressed, and translated 3 units to the right and 1 unit down.

300

Michelle transforms the quadratic parent function by vertically stretching the parabola by a factor of 5. Then, she translates the parabola 9 units up and 4 units right. What is the equation of Michelle's parabola?

y = 5(x-4)² +9

400

Describe the transformation.

y = -1/2(x + 6)² - 2

Vertically compressed by a factor of 1/2, reflected across the x-axis, translated left 6 units, and translated down 2 units.