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Complete the Square

Complete the Square. Objective I can find zeros by completing the square. Warm Up. Rewrite the following as perfect squares. 1. x 2 + 14x + 49 ( _______) 2 2. x 2 -2x + 1 (________) 2. Our goal. What if you were asked to complete the pattern of a perfect square. x 2 + 20x + ____

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Complete the Square

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  1. Complete the Square Objective I can find zeros by completing the square

  2. Warm Up • Rewrite the following as perfect squares. • 1. x2 + 14x + 49 • ( _______)2 • 2. x2 -2x + 1 • (________)2

  3. Our goal • What if you were asked to complete the pattern of a perfect square. • x2 + 20x + ____ • ( )2 • OYO • x2 -18x + ______ • (_______)2 This Process is called “Completing the Square” because our goal is to figure out what number you need to create a perfect square.

  4. Not So Perfect Squares. • Some equations aren’t as easy to see what value will complete the square such as. • For these we use • (b/2)2 • Look back at the previous complete the square problems, how does the constant term of the factored binomial relate to the middle term? • What will be the factored form of this quadratic? x2 + 9x +

  5. Find . Check It Out! Example 2c Complete the square for the expression. Write the resulting expression as a binomial squared. x2 + 3x + CheckFind the square of the binomial. Add. Factor.

  6. Why? • We can use completing the square for two things. • Solve quadratics by means of the square root property. • Transform a function in standard form to vertex form. • For this unit we will focus on solving equations by completing the square.

  7. You can complete the square to solve quadratic equations.

  8. Solve the equation by completing the square. x2= 12x- 20

  9. Solve the equation by completing the square. 18x + 3x2 = 45

  10. Solve the equation by completing the square. 2x2 + 8x = 12

  11. Solve the equation by completing the square. 5x2 + 10x – 7 = 0

  12. OYO Solve the equation by completing the square. 3x2 – 24x = 27

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