Obj: graph parabolas in two forms

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Essential Question: How do you determine whether a quadratic function has a maximum or minimum and how do you find it?

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Presentation transcript:

Obj: graph parabolas in two forms Chapter 3 3.1 Quadratic Functions Obj: graph parabolas in two forms and find the max or min

Quadratic Functions Review Quadratic form Solving a quadratic Graph Vertex Axis of Symmetry Standard Form

Finding Standard Form Given the function find the standard form by completing the square. 1. Factor a from the first two terms. 2. Complete the square as in last chapter. 3. Keep the equation in balance! 4. Factor the square and simplify. 5. Standard form

Find Vertex and Axis of Symmetry Standard form vertex at (h, k) vertex = ( , ) axis of symmetry at x = h axis at x = Quadratic form vertex at axis of symmetry at x = -b/2a

Maximum and Minimum The max or min is the y-value of the vertex. If a > 0, the function has a minimum. If a < 0, the function has a maximum. To find the max or min: find the vertex by one of the previous methods or . . Use the graphing calculator

Example Find the maximum or minimum value of the quadratic function. State whether the value is a maximum or minimum. By hand: With calculator:

Assignment Page 343 1 – 41 e.o.o., 59, 65