 # Intercept, Standard, and Vertex Form

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Intercept, Standard, and Vertex Form
Unit 1: Solving Intercept Form Converting Standard and Vertex Form

Different Ways to Write a Quadratic
Standard Form Y = ax2 + bx + c Vertex x = –b/2a, plug in to find y Vertex Form Y = a(x – p) (x – q) The x-intercepts are p and q Axis of symmetry is the midpoint of p and q Intercept Form Y = a(x – h)2 + k Vertex at (h,k)

Intercept Standard Write the Equation In Standard Form
Ex1: Y = -(x + 4) (x – 9) FOIL -(x2 -9x +4x – 36) -(x2 -5x – 36) Multiply –x2 + 5x + 36

Intercept Standard Ex2: Write the Equation in Standard Form
-2(x + 4)(x – 3) Foil -2(x2 -3x + 4x – 12) Multiply -2(x2+ x - 12) -2x2 -2x + 24

Vertex Standard EX1: Convert to Standard form 3(x – 1)2 + 8 Foil
3 (x - 1) (x -1) + 8 3 (x2 – 1x – 1x + 1) + 8 3(x2 – 2x + 1) + 8 Multiply 3x2 – 6x Add 3x2 – 6x +11

Vertex Standard You try…. EX2: Convert to standard form
Y = (x+ 2)2 – 7 Foil (x +2) (x+2) – 7 (x2 + 2x + 2x + 4) – 7 (x2 + 4x +4) - 7 Add/subtract x2 +4x -3

Standard vertex Y = x2 – 2x – 1……… y = a(x-h)2 + k
h: Calculate (-b/2a) -(-2) = = 1 2(1) k: plug answer (-b/2a) into equation Y = (1)2 -2(1) – 1 Y = 1 – 2 – 1 = -2 a: “a” is the original “a” from standard form a = 1 Rewrite Equation: Y = 1(x – 1)2 -2

Standard vertex Y = 2x2 – 12x + 19……… y = a(x-h)2 + k
h: Calculate (-b/2a) -(-12) = = 3 2(2) k: plug answer (-b/2a) into equation Y = 2(3)2 -12(3) + 19 Y = 18 – = 1 a: “a” is the original “a” from standard form a = 2 Rewrite Equation: Y = 2(x – 3)2 + 1