+ Completing the Square and Vertex Form. + Completing the Square.

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Presentation transcript:

+ Completing the Square and Vertex Form

+ Completing the Square

+ Perfect Square Trinomials Quadratic Trinomials with a repeated factor! X x + 25 X 2 – 16x + 64 X x + 81

+ Solving a Perfect Square Trinomial We can solve a Perfect Square Trinomial using square roots. X x + 25 = 36

+ Solving a Perfect Square Trinomial X 2 – 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 Square Using the formula for completing the square, turn each trinomial into a perfect square trinomial.

+ Solving by Competing the Square Solve by completing the square: X 2 + 6x + 8 = 0

+ Solving by Competing the Square Solve by completing the square: X 2 – 12x + 5 = 0

+ Solving by Competing the Square Solve by completing the square: X 2 – 8x + 36 = 0

+ Vertex Form

+ Standard form vertex

+ Vertex Vertex: highest or lowest point on the graph. 2 ways to find Vertex: 1) Calculator: 2 nd  CALC MIN or MAX 2) Algebraically

+ Find the Vertex 1) x 2 + 8x + 1 2) x 2 + 2x – 5 3) 2x 2 – 10x + 3

+ Complete the Square Investigation Step 1: Complete the square: X 2 + 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) x 2 + 6x + 8 = 0 2) X 2 – 2x + 10 = 0

+ Vertex Form

+ Converting from Standard to Vertex Standard: y = ax 2 + bx + c Things you will need: a = and Vertex: Vertex: y = a(x – h) 2 + k

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

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

+ Now Convert and Solve Convert each quadratic from standard to vertex form. Then Solve for x. 1. x 2 + 6x – 5 = 0

+ Now Convert and Solve Convert each quadratic from standard to vertex form. 1. 3x 2 – 12x + 7 = x 2 + 4x – 3 = 0