Show:
Quadratics in Standard Form
Quadratics in Vertex Form
Quadratics in Factored Form
Conversions
Complete the Square
100

The standard form of quadratics

y=ax^2+bx+c

100

The vertex form of quadratics

y=a(x-h)^2+k

100

The factored form of x2+5x+6

(x+2)(x+3)

100

The process to convert quadratics in standard form to quadratics in vertex form

completing the square


 

100

Rewrite into vertex form by completing the square:

x2-4x+8

What is the vertex?

(x-2)2+4

Vertex: (2, 4)

200

Calculate the x-value of the vertex of

x2-10x+6

h= 5

200

Vertex of

y = a (x - h)^2 + k

(h, k)

200

The factored form of

x^2-6x+8

(x-2)(x-4)

200

The first step in converting a vertex form into standard form (i.e. converting y=(x-4)2+3)

FOIL

200

Rewrite into vertex form by completing the square:

x2-12x+34

What is the vertex?

(x-6)2+2

(6, 2)

300

Calculate the x-value of the vertex of:

2x2+8x-3

h= -2

300

The vertex of 

-2 (x - 4)^2 + 2

(4,2)

300

The factored form of x2-10x+25

(x-5)2

300

What are a, b, and c of standard form for:

(x+3)2-4

x2+6x+5

a=1

b=6

c=5

300

Rewrite into vertex form by completing the square:

x2-10x+19

What is the vertex?

(x-5)2+6

(5, 6)

400

Calculate the x-value of the vertex of:

5x2+15x+67

h= -3/2 or -1.5
400

The  Vertex of

y = 2(x-3)^2 - 8

(3, -8)

400

The factored form of 2x2+5x+3

(2x+3)(x+1)

400

What are a, b, and c of standard form for:

(x-2)2+2

x2-4x+6

a=1

b=-4

c=6

400

Rewrite into vertex form by completing the square:

2x2-8x+8

What is the vertex?

2(x-4)2

(4, 0)

500

Calculate the x value of the vertex:

-2t2-12t+15

h=-3

500

Vertex of 

-4 (x + 6)2 - 4

(-6, -4)

500

The form of a perfect square trinomial

x2+bx+(b/2)2

500

What are a, b, and c of standard form for:

(x+7)2-40

x2+14x+9

a=1

b=14

c=9

500

Rewrite into vertex form by completing the square:

3x2-18x+40

What is the vertex?

3(x-3)2+13

(3, 13)