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5.4 – Completing the Square Objectives: Use completing the square to solve a quadratic equation. Use the vertex form of a quadratic function to locate the axis of symmetry of its graph. Standard: 2.8.11.N. Solve quadratic equations symbolically and graphically

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Example 1

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Example 1 c and d c. x 2 – 7x The coefficient of x is -7 ½ (-7) = Thus the perfect square trinomial is d. x 2 + 16x The coefficient of x is 16 ½ (16) = 8 (8) 2 = 64 Thus the perfect square trinomial is

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Solving Equations by Completing the Square STEPS: Make sure A = 1. Bring the C to the Zero side. Complete the Square meaning “ take ½ of B and Square It.” Add the answer you got from complete the square on the other side so you keep the equation balanced. Put the complete the square side into perfect square notation. Solve the equation.

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Example 2a

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Example 2b * x 2 + 10x – 24 = 0

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Example 2c * 2x 2 + 6x = 7

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Example 2d * 3x 2 – 6x = 5

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VERTEX FORM Vertex Form If the coordinates of the vertex of the graph of y = ax 2 + bx + c, where a ≠ 0, are (h,k), then you can represent the parabola as y = a(x – h) 2 + k, which is the vertex form of a quadratic equation.

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Another Vertex Form Problem! Given g(x) = 3x 2 – 9x – 2, write the function in vertex form, and give the coordinates of the vertex and the equation of the axis of symmetry. Then describe the transformations from f(x) = x 2 to g.

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Writing Questions

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Homework Pg. 304 #12-46 even

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