1. Section 3.5: Convert Standard to Vertex Form
Objectives:
• Learn how to “complete the square”
• Convert standard form of a
quadratic to vertex form.

3. Concept: Other Quadratic Forms
Vertex form y = a (x – h)2 + k
Then (h,k) is the vertex
Given f(x) = –3x2 – 12x – 13
Change to vertex form
Hint, use completing the square

4. Concept: Vertex Form by Completing the Square
y = -3x2 – 12x - 13 1.
Move the constant (C) to the opposite side.
y + 13 = –3x2 – 12x
_____ _____
– –3
Vertex (-2, -1)
a = -3 2.
Factor out A from each of the remaining terms.
y + 13 = –3(x2 + 4x) 3.
Find (– )2 where B is the coefficient of x 4.
Add this to the right side of the equation
y ___ = –3(x2 + 4x + ___) 4

5. Concept: Vertex Form by Completing the Square cont…
y ___ = –3(x2 + 4x + ___) 4 5.
Multiply that number by the A and add the product to the opposite side.
y ____ = –3(x2 + 4x + 4 )
–12
y + 1 = –3(x2 + 4x + 4) 6.
Simplify the left side
√x2 √4 7.
Factor the right side
y + 1 = –3( )2 x + 2

6. Concept: Vertex Form by Completing the Square cont…
y + 1 = –3( x + 2 )2
– –1 8.
Get y alone
y = –3(x + 2)2 – 1