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Exploring Quadratic Functions: Maximum Values, Zeros, and Outputs

This instructional guide focuses on quadratic functions, providing step-by-step techniques to find maximum values, zeros, and specific outputs. It covers essential concepts like the vertex form of a quadratic equation and how to use factoring and the Zero Product Property (ZPP) effectively. The chapter review reinforces these concepts with practical problems, including determining minimum values, solving equations by completing the square, and analyzing function graphs. Homework assignments and resources for further learning are also included to enhance understanding.

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Exploring Quadratic Functions: Maximum Values, Zeros, and Outputs

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  1. Warm Up # 1 Find the maximum value of the function. # 2 Find the zeros of the function. # 3 Find the input(s) of the function that give an output of 9.

  2. Warm Up # 1 Find the maximum value of the function. Maximum Output The Vertex

  3. Warm Up # 1 Find the maximum value of the function. The Vertex

  4. Warm Up # 1 Find the maximum value of the function. The Vertex What’s the range?

  5. Warm Up # 2 Find the zeros of the function. Factor Apply the ZPP

  6. Warm Up # 3 Find the input(s) of the function that give an output of 9. Factor Apply the ZPP

  7. Chapter Review Match each function with its graph. # 1 # 2 # 3 # 4

  8. Chapter Review What is the minimum value of the function below? # 5

  9. Chapter Review # 6

  10. Chapter Review B D A C Which quadratic equation has the solutions # 7

  11. Chapter Review How many times does the graph of intersect the x-axis? # 8

  12. Chapter Review To correctly solve the equation by completing the square, which equation is part of the solution process? # 9

  13. Chapter Review # 10

  14. Chapter Review Today’s homework is on page 607: 2-13. Look for a video on Mr. Devor’s website to teach you about the discriminant. The next fours slides are a review of how we “derived” the quadratic formula!

  15. Deriving the Quadratic Formula Quadratic equation in Standard Form Complete The Square Divide through by a

  16. Deriving the Quadratic Formula Quadratic equation in Standard Form Complete The Square Divide through by a Make room to complete the square

  17. Deriving the Quadratic Formula Quadratic equation in Standard Form Complete The Square Divide through by a Make room to complete the square Find the squared binomial: Complete the square: Balance the equation Add the terms on the right side of the equation and simplify

  18. Deriving the Quadratic Formula Quadratic Formula Equation re-written as a squared binomial Isolate x by using square roots Take the square root of the left side Take the square roots of the right side Simplify the radical expression Get x alone on one side of the equation Simplify by adding the terms on the right side

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