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Graphing Quadratics

100

What is the axis of symmetry?

x^2+3x-4=0

x=-3/2

200

What is the vertex?

2x^2+4x-5=0

(-1,-8)

300

What is the axis of symmetry, the vertex and the y intercept? Sketch the graph of the quadratic. 

3x^2+12x-8=0

x=-2

(-2,-20)

(0,-8)

400

What is the vertex?

Does the graph have a minimum or a maximum? How do you know?

What is that value?

What are the solutions?

x^2+16x+63=0

(-8,-1)

Minimum faces up

(-8,-1)

(-9,0) and (-7,0)

500

What is the vertex?

Does the graph have a minimum or maximum?

What is it?

Make a table to find the solutions.

Sketch the graph.

x^2-3x-10=0

(-1.5,-3.25)

Minimum (-1.5,-3.25)

(5,0)(-2,0)

Solving by Factoring

100

Solve by Factoring

x^2+5x+6=0

x=-2

x=-3

200

Solve by Factoring

x^2-3x-40=0

x=8

x=-5

300

Solve by Factoring

2x^2-5x-3=0

x=-1/2

x=3

400

Solve by Factoring

6x^2+7x-20=0

x=4/3

x=-5/2

500

Solve by Facoring

8x^2+2x=3

x=1/2

x=-3/4

Imaginary Numbers

100

Simplify 

(2+3i)-(4-6i)

-2+9i

200

Simplify

(2-5i)(4+7i)

43-6i

300

Simplify 

2/3i

2i/-3

400

Simplify

i^67

-i

500

Simplify 

(2i+1)/(6i-4)

(-16-2i)/-52

Completing the Square and Solving by Square Root Method

100

Solve by Square root method 

x^2+25=0

x=+- 5i

200

Solve by Square root method

3x^2+27=0

x=+-3i

300

Solve by completing the square 

x^2+14x+49=0

x=-7

400

Solve with square root method

x^2+16x-60=0

x=3.14

x=-19.14

500

Solve with square root method

x^2+20x+130=5

x=-10+5i

x=-10-5i

Quadratic Formula

100

2x^2+3x-10=0

What is the determinant?

89

200

What is the determinant?

How many solutions will the quadratic have?

-x^2-7x-14=0

-7

2 Imaginary Solutions

300

What is the determinant?

How many solutions will there be?

x^2-5x-19=0

Discriminant = 101

2 Real Solutions

400

What is the discriminant?

How many solutions will there be?

What are the solutions?

3x^2+2x-13=0

160

2 real 

x=1.77

x=-2.44

500

What is the discriminant?

How many solutions will there be?

What are the solutions?

x^2-12x=-40

Discriminant = -16

2 imaginary

12+4i/2 and 12-4i/2