Intercept, Intercept, Standard, and Standard, and Vertex FormVertex FormUnit 1: Solving Intercept FormUnit 1: Solving Intercept Form

Converting Standard and Converting Standard and Vertex Form Vertex Form

Different Ways to Write a Different Ways to Write a Quadratic Quadratic

Standard FormStandard Form Y = axY = ax22 + bx + c + bx + c

Vertex x = –b/2a, plug in to find yVertex x = –b/2a, plug in to find y

Vertex FormVertex Form Y = a(x – p) (x – q) Y = a(x – p) (x – q)

The x-intercepts are p and qThe x-intercepts are p and q Axis of symmetry is the midpoint of p and qAxis of symmetry is the midpoint of p and q

Intercept FormIntercept Form Y = a(x – h)Y = a(x – h)22 + k + k

Vertex at (h,k)Vertex at (h,k)

Intercept StandardIntercept Standard

Write the Equation In Standard Form Write the Equation In Standard Form Ex1: Y = -(x + 4) (x – 9)Ex1: Y = -(x + 4) (x – 9)

FOIL FOIL -(x-(x22 -9x +4x – 36) -9x +4x – 36) -(x-(x22 -5x – 36) -5x – 36)

Multiply Multiply ––xx22 + 5x + 36 + 5x + 36

Intercept StandardIntercept Standard

Ex2: Write the Equation in Standard FormEx2: Write the Equation in Standard Form

-2(x + 4)(x – 3)-2(x + 4)(x – 3) FoilFoil -2(x-2(x22 -3x + 4x – 12) -3x + 4x – 12) Multiply Multiply -2(x-2(x22+ x - 12) + x - 12) -2x-2x22 -2x + 24 -2x + 24

Vertex Vertex StandardStandard

EX1: Convert to Standard formEX1: Convert to Standard form 3(x – 1)3(x – 1)22 + 8 + 8 FoilFoil

3 (x - 1) (x -1) + 83 (x - 1) (x -1) + 8 3 (x3 (x22 – 1x – 1x + 1) + 8 – 1x – 1x + 1) + 8 3(x3(x22 – 2x + 1) + 8 – 2x + 1) + 8

MultiplyMultiply 3x3x2 2 – 6x + 3 + 8– 6x + 3 + 8

AddAdd 3x3x22 – 6x +11 – 6x +11

Vertex Vertex StandardStandard

You try…. You try…. EX2: Convert to standard formEX2: Convert to standard form

Y = (x+ 2)Y = (x+ 2)22 – 7 – 7 Foil (x +2) (x+2) – 7Foil (x +2) (x+2) – 7 (x(x22 + 2x + 2x + 4) – 7 + 2x + 2x + 4) – 7 (x(x22 + 4x +4) - 7 + 4x +4) - 7

Add/subtractAdd/subtract xx22 +4x -3 +4x -3

Standard vertexStandard vertex

Y = xY = x22 – 2x – 1……… y = a(x-h) – 2x – 1……… y = a(x-h)2 2 + k+ k h:h: Calculate (-b/2a) Calculate (-b/2a)

-(-2)-(-2) = = 22 = 1 = 1 2(1) 22(1) 2

k:k: plug answer (-b/2a) into equation plug answer (-b/2a) into equation Y = (1)Y = (1)22 -2(1) – 1 -2(1) – 1 Y = 1 – 2 – 1 = -2Y = 1 – 2 – 1 = -2

a: a: “a” is the original “a” from standard form“a” is the original “a” from standard form a = 1a = 1

Rewrite Equation:Rewrite Equation: Y = Y = 11(x – (x – 11))22 -2-2

Standard vertexStandard vertex

Y = 2xY = 2x22 – 12x + 19……… y = a(x-h) – 12x + 19……… y = a(x-h)2 2 + k+ k h:h: Calculate (-b/2a) Calculate (-b/2a)

-(-12)-(-12) = = 1212 = 3 = 3 2(2) 42(2) 4

k:k: plug answer (-b/2a) into equation plug answer (-b/2a) into equation Y = 2(3)Y = 2(3)22 -12(3) + 19 -12(3) + 19 Y = 18 – 36 +19 = 1Y = 18 – 36 +19 = 1

a: a: “a” is the original “a” from standard form“a” is the original “a” from standard form a = 2a = 2

Rewrite Equation:Rewrite Equation: Y = Y = 22(x – (x – 33))22 + 1+ 1