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

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

Concept: Vertex Form by Completing the Square y = -3x2 – 12x - 13 1. Move the constant (C) to the opposite side. +13 +13 y + 13 = –3x2 – 12x _____ _____ –3 –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 + 13+ ___ = –3(x2 + 4x + ___) 4

Concept: Vertex Form by Completing the Square cont… y + 13+ ___ = –3(x2 + 4x + ___) 4 5. Multiply that number by the A and add the product to the opposite side. y + 13+ ____ = –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

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