+ completing the square and vertex form. + completing the square
DESCRIPTION
+ Perfect Square Trinomials Quadratic Trinomials with a repeated factor! X x + 25 X 2 – 16x + 64 X x + 81TRANSCRIPT
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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