Quadratics

Quadratics in Standard Form

100

The standard form of quadratics

y=ax^2+bx+c

200

Calculate the x-value of the vertex of

x²-10x+6

h= 5

300

Calculate the x-value of the vertex of:

2x²+8x-3

x = -8/2(2)  = -2 

h= -2

400

Calculate the x-value of the vertex of:

5x²+15x+67

x = -b/2a = -15/2(5) = -3/2 

h= -3/2 or -1.5

500

Calculate the x value of the vertex:

-2t²-12t+15

x = -b/2a  = 12/2(-2) = 12/-4 = -3

h=-3

Quadratics in Vertex Form

100

The vertex form of quadratics

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

200

Vertex of

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

(h, k)

300

The vertex of 

-2 (x - 4)^2 + 2

(4,2)

400

The  Vertex of

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

(3, -8)

500

Vertex of 

-4 (x + 6)² - 4

(-6, -4)

Quadratics in Factored Form

100

The factored form of x²+5x+6

(x+2)(x+3)

200

The factored form of

x^2-6x+8

(x-2)(x-4)

300

The factored form of x²-10x+25

(x-5)²

400

The factored form of 2x²+5x+3

(2x+3)(x+1)

500

The form of a perfect square trinomial

x²+bx+(b/2)²

Conversions

100

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

completing the square

 

200

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

FOIL

300

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

(x+3)²-4

x²+6x+5

a=1

b=6

c=5

400

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

(x-2)²+2

x²-4x+6

a=1

b=-4

c=6

500

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

(x+7)²-40

x²+14x+9

a=1

b=14

c=9

Complete the Square

100

Rewrite into vertex form by completing the square:

x²-4x+8

What is the vertex?

(x2 - 4x) + 8

(b/2)² = -4/2 = (-2)^{2 =} 4  Note:add 4 to inside ( ) 

(x² - 4x + 4)  + 8 - 4 Note: -4 from outside ()

(x-2)²+4

Vertex: (2, 4)

200

Rewrite into vertex form by completing the square:

x²-12x+34

What is the vertex?

(x²-12x +   ) + 34 Find (b/2)²⁼(-12/2)² =(-6)²= 36

(x²-12x + 36 ) + 34 - 36 

(x-6)² - 2

(6, -2)

300

Rewrite into vertex form by completing the square:

x²-10x+19

What is the vertex?

(x² -10x       ) + 19   _(-10/2)² _{= (-5)}²

^{(x2 -10x + 25 )   + 19 - 25   Note: Add 25 inside ( ) subtract outside}

(x-5)^{2 -} 6

(5, -6)

400

Rewrite into vertex form by completing the square:

2x²-8x+8

What is the vertex?

(2x²- 8x) Factor out 2   2(x²- 4x       ) + 8

(-4/2)²=(-2)²= 4  add 4(2) inside & subtract 4(2) 

2(x²- 4x + 4) + 8 - 8

2(x-2)²      Vertex (2, 0)

500

Rewrite into vertex form by completing the square:

What is the vertex?

(3x²-18x) + 40 Factor out 3(x²- 6x +    )  + 40 

(-6/2)²=(-3)² =9.. 3(9)=27, +27inside, -27outside

3(x²- 6x + 9)  + 40 - 27

3(x-3)²+13

(3, 13)