Solving Quadratic Equations

Factoring & Characteristics of Parabola

100

What are the factors of 

y = x² -5x - 14 ?

(x - 7)(x + 2)

200

What are the x-intercepts of the graph 

y = x²+3x+2 ? 

x = -2 x = -1

300

What are the solutions for the quadratic equation 

x² - 2x = 24 ?

-4, 6

400

For the graph: 

y = 2x² + 12x - 10

a) What is the y-intercept?

b) What is the axis of symmetry?

a) y-intercept: - 10

b) axis of sym: x = -3

500

Find the x-values: 

y = x² + 3x - 50

y = 2x - 20

x = 5, x = -6

Square Roots & Imaginary Numbers

100

Solve the following quadratic equation by using square roots: 

x² = 4

x = 2 x = -2

200

Solve the following quadratic equation by using square roots: 

2x² = -72

+6i or -6i

300

Solve the following quadratic equation by using square roots: 

4x² - 5 = 395

x = 10 x = -10

400

What is the product of 

(11 + 2i) and (12 - 14i)?

160 - 130i

500

Solve the following quadratic equation by using square roots: 

-3(x-1)² + 3 = 123 

x = 1 +- 2i sqrt(10)

Completing the Square

100

What number should be added to both sides to complete the square for 

x² + 6x = -8 ?

9

200

Solve the following quadratic equation by completing the square: 

x² - 6x = -5

x = 1 x = 5

300

Solve the following quadratic equation by completing the square: 

x² - 12x + 48 = 0

x = 6 +- 2i sqrt(3)

400

Write the following in vertex form: 

y = 2x² + 12x +16 

y = 2(x+3)² - 2

500

Solve the following quadratic equation by completing the square: 

2x² - 8x = 10

x = 5 x = -1

Quadratic Formula

100

What is the quadratic formula?

x = -b +- sqrt(b² - 4ac) /(2a)

200

How many times does the graph of the parabola for 

y = 2x² - 5x + 1 cross the x-axis?

twice

300

How many times does the graph of the function

y = -4x² + 2x - 1 intersect the x-axis?

none

400

Solve the following quadratic equation by using the quadratic formula: 

2x² - 3x - 3  = 0

x = 3/4 +- (sqrt(33))/4

500

Solve the following quadratic equation by using the quadratic formula: 

4x² - 2x + 3 = 0

x = 1/4 +- (i sqrt(11))/4

Vertex and Review

100

Find the vertex of 

f(x)=-x²+8x-15

(4,1)

200

Find the vertex of 

f(x)=x² - 2x

(1,-1)

300

Solve the system:

6x + y = 32

2x + 8y = -20

(6, -4)

400

f(x)= -x² - 4x + 6

(-2,10)

500

It costs $135 for a season pass to Knott's and a individual day ticket costs $32 without the pass. What is the minimum number of times you should go to Knott's in order for the cost of the pass to be less than the total cost of buying an individual ticket for each time he attends.

5 times