Solving Quadratic Equations

Factoring

100

Use the Zero Product Property to solve the following quadratic equation. (x - 7)(x + 2) = 0

x = 7 x = -2

200

Solve the following quadratic equation by factoring. x²+3x+2 = 0

x = -2 x = -1

300

Solve the following quadratic equation by factoring. 2x² - 8x = 0

x = 0 x = 4

400

Solve the following quadratic equation by factoring. x² - 6x - 27 = 0

x = 9 x = -3

500

Solve the following quadratic equation by factoring. x² -17x +30 = 0

x = 2 x = 15

Square Roots

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: (x-10)² = 49

x= 3 x=17

300

Solve the following quadratic equation by using square roots: 4(x+2)²=36

x = -5 x = 1

400

Solve the following quadratic equation by using square roots: x² -12 = 0

*** You must simplify the square root***

x= + 2*sqrt(3) x= - 2*sqrt(3)

500

Solve the following quadratic equation by using square roots: 5x² + 3 = 128

x = 5 x = -5

Completing the Square & Vertex

100

Identify the vertex of the following equation: 

y=(x-5)²+2

Vertex: (5, 2)

200

Identify the vertex and the axis of symmetry of the following equation: 

y=2.4(x+8)²-10

Vertex: (-8, -10)

Axis of symmetry: x= -8

300

Complete the square to make a perfect square trinomial: x²+20x+_______

Hint: find (b/2a)²

x²+20x+100

400

Complete the square to make a perfect square trinomial: x²+30x+_______

Hint: find (b/2a)²

x²+30x+225

500

Complete the square to make a perfect square trinomial: x²+11x+_______

Hint: find (b/2a)²

x²+11x+(121/4)

Quadratic Formula

100

Solve the following quadratic equation by using the quadratic formula: x² -9x + 20 = 0

x = 5 x = 4

200

Solve the following quadratic equation by using the quadratic formula: x² + 6x + 5 = 0

x = -1 x = -5

300

Solve the following quadratic equation by using the quadratic formula: 4x² - 17x = 15

x = 5 x = -3/4

400

Solve the following quadratic equation by using the quadratic formula: 2x² = -9x - 4

x = -1/2  x = -4

500

Solve the following quadratic equation by using the quadratic formula: x²-4x-3= 0

x = 2 + sqrt(7) x = 2 - sqrt(7)

Discriminant & Imaginary Numbers

100

What is i³?

-i

200

***Daily Double***

2 Parts:

1) What is the conjugate of -6 - 5i? 

2) Simplify 4i/(3+7i)

1) -6 + 5i

2) (6i+14)/29 or can have (12i+28)/58

300

Simplify: (5-2i)(6+5i)

40+ 13i

400

Identify the discriminant of the below equation, and use the discriminant to determine the number and type (real or complex)  of solutions.

2x²+3x-2=0

D=25

There will be 2 real solutions. 

500

Identify the discriminant of the below equation, and use the discriminant to determine the number and type (real or complex)  of solutions.

3x²+1=-2x

D= -8

There will be 2 complex solutions (0 real solutions)