All about Quadratics (WHS)

Converting

100

Convert to standard form: y=(x+2)(x-1)

y=x²+x-2

200

Convert to factored form: y=2x²+3x-5

y=(2x+5)(x-1)

300

Convert to vertex form: y=x²-4x+6

y=(x-2)²+2

400

Convert to standard form: y=3(x-2)²+4

y=3x²-12x+16

500

Convert to vertex form: y=2x²+16x+8

y=2(x+4)²-24

Key Features

100

What is the y-intercept of x²-3x+4? 

(0,4)

200

What are the x-intercepts of y=(2x-3)(x+2)? 

(3/2,0) and (-2,0)

300

What is the vertex of 3(x+1)²-8?

(-1,-8)

400

What is the equation of the Axis of Symmetry? y=2x²-4x+5

x=1

500

What is the vertex? y=(x-3)(x+1)

(1,-4)

Solve by any method

100

v²+2v-8=0

2 and -4

200

4(x+1)²=16

1 and -3

300

x²+2x-24=0

-6 and 4

400

x²-3x+9=0

  x=(3+-3isqrt(3))/2

500

2x²+7x=-5

(-1,0) and (-5/2,0)

Quadratic Formula

100

Solve by using the Quadratic Formula 

x²+2x-1=0

 x=-1+-sqrt(2) 

200

Solve by using the Quadratic Formula 

2x²-9x-5=0

x = 5 , -1/2

300

Solve by using the Quadratic Formula 

6x²-7x+6=0

  x=(7+-isqrt(95))/12

400

Solve by using the Quadratic Formula 

x²+2x=5

 x=-1+-sqrt(6) 

500

Solve by using the Quadratic Formula 

2x²+11x+ 9=0

x = -1, -9/2

Solve by Factoring

100

Solve the Quadratics by Factoring

x²+2x=3

x=-3, x=1

200

Solve the Quadratics by Factoring 

x²+16=10x

x=2, x=8

300

Solve the Quadratics by Factoring

6n²-n=2

x=-1/2, x=2/3

400

Solve the Quadratics by Factoring

4x²-25=0

x=5/2 and x=-5/2

500

Explain why the following quadratic is not factorable.

y=x²-4x+5

There are no two numbers that multiply to 5 and add to -4.