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Warm-Up: December 15, 2011 Divide and express the result in standard form

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Homework Questions?

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Quadratic Functions Section 2.2

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Quadratic Functions A quadratic function is any function that can be written in the form The graph of a quadratic function is a parabola. Every parabola has a vertex at either its minimum or its maximum. Every parabola has a vertical axis of symmetry that intersects the vertex.

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Example Graphs Vertex Axis of Symmetry

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Standard Form of a Quadratic Function Vertex is at (h, k) Axis of symmetry is the line x=h If a>0, the parabola opens upward, U If a<0, the parabola opens downward,

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Graphing Quadratics in Standard Form 1. Determine the vertex, (h, k) 2. Find any x-intercepts by replacing f(x) with 0 and solving for x 3. Find the y-intercept by replacing x with 0 4. Plot the vertex, axis of symmetry, and y-intercepts and connect the points. Draw a dashed vertical line for the axis of symmetry. 5. Check the sign of “a” to make sure your graph opens in the right direction.

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Example 1 Graph the quadratic function. Give the equation of the parabola’s axis of symmetry. Determine the graph’s domain and range.

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You-Try #1 Graph the quadratic function. Give the equation of the parabola’s axis of symmetry. Determine the graph’s domain and range

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Graphing Quadratics in General Form General form is The vertex is at x-intercepts can be found by quadratic formula (or sometimes by factoring and zero product property) y-intercept is at (0, c) Graph the parabola using these points just as we did before.

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Example 3 Graph the quadratic function. Give the equation of the parabola’s axis of symmetry. Determine the graph’s domain and range

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You-Try #3 Graph the quadratic function. Give the equation of the parabola’s axis of symmetry. Determine the graph’s domain and range

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Minimum and Maximum Consider If a>0, then f has a minimum If a<0, then f has a maximum The maximum or minimum occurs at The maximum or minimum value is

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Example 4 (Page 266 #44) A football is thrown by a quarterback to a receiver 40 yards away. The quadratic function models the football’s height above the ground, s(t), in feet, when it is t yards from the quarterback. How many yards from the quarterback does the football reach its greatest height? What is that height?

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You-Try #4 (Page 266 #43) Fireworks are launched into the air. The quadratic function models the fireworks’ height, s(t), in feet, t seconds after they are launched. When should the fireworks explode so that they go off at the greatest height? What is that height?

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Assignment Page 264 #1-8 ALL (use your graphing calculator for 5-8), #9-41 Every Other Odd

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