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Completing the Square and Vertex Form

+Completing the Square

+Perfect Square TrinomialsQuadratic Trinomials with a repeated factor!X2 + 10x + 25

X2 – 16x + 64

X2 + 18x + 81

+Solving a Perfect Square Trinomial We can solve a Perfect Square

Trinomial using square roots.X2 + 10x + 25 = 36

+Solving a Perfect Square Trinomial X2 – 14x + 49 = 81

+What if it’s not a Perfect Square Trinomials?!If an equation is NOT a perfect square Trinomial, we can use a method called COMPLETING THE SQUARE.

+Completing the SquareUsing the formula for completing the square, turn each trinomial into a perfect square trinomial.

+Solving by Competing the SquareSolve by completing the square:

X2 + 6x + 8 = 0

+Solving by Competing the SquareSolve by completing the square:X2 – 12x + 5 = 0

+Solving by Competing the SquareSolve by completing the square:X2 – 8x + 36 = 0

+Vertex Form

+Standard form vertex

+Vertex Vertex: highest or lowest point on the graph.2 ways to find Vertex:1) Calculator: 2nd CALCMIN or MAX2) Algebraically

+Find the Vertex1) x2 + 8x + 1

2) x2 + 2x – 5

3) 2x2 – 10x + 3

+Complete the Square InvestigationStep 1: Complete the square:

X2 + 4x – 4 = 0

Step 2: DON’T SOLVE! Instead get zero on one side.

Step 3: graph the non-zero side and find the vertex

+Completing the Square Finds the vertex!

Use completing the square to find the vertex of each:1) x2 + 6x + 8 = 0

2) X2 – 2x + 10 = 0

+Vertex Form

+Converting from Standard to VertexStandard: y = ax2 + bx + cThings you will need:

a = and Vertex:

Vertex: y = a(x – h)2 + k

+Example

Convert from standard form to vertex form.y = -3x2 + 12x + 5

+Example

Convert from standard form to vertex form.y = x2 + 2x + 5

+Now Convert and SolveConvert each quadratic from standard to vertex form. Then Solve for x.1. x2 + 6x – 5 = 0

+Now Convert and Solve

Convert each quadratic from standard to vertex form.1. 3x2 – 12x + 7 = 0

2. -2x2 + 4x – 3 = 0