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10.5 & 10.5 Extension 10.5 Solve Quadratic Equations by Completing the Square 10.5 Extension Write Quadratic Functions in Vertex form and Graph the Functions
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10.5 Example 1 Complete the Square
Find the value of c that makes the expression a perfect square trinomial. Then write the expression as the square of a binomial. a. x2 + 8x + c b. x2 – 5x + c
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Example 2- Solving Equations
Solve by Completing the Square. a. x2 – 16x = b. x2 + 2x = 3
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Example- Solve a Quadratic Equation in standard form
Solve by Completing the Square. Round answers to the nearest hundredth. a. m2 + 10m + 8 = 0 b. 3g2 – 24g + 27 = 0
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Example 4- Story Problems
Crafts You decide to use chalkboard paint to create a chalkboard on a door. You want the chalkboard to have a uniform border as shown. You have enough chalkboard paint to cover 6 square feet. Find the width of the border to the nearest inch.
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Another Story Problem Solve by completing the square. The given triangle has an area of 108m2. Find the value of x. X m X + 6 m
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10.5 Extension
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10.5 Extension- Example 1 y = (x + 1)2 - 1
Graph the quadratic function. Label the vertex and axis of symmetry. y = (x + 1)2 - 1
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10.5 Extension- Example 2 y = x2 – 4x + 3
Write the function in vertex form, then graph the function. Label the vertex and axis of symmetry. y = x2 – 4x + 3
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