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

2. 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)

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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