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Warm-Up: December 15, 2011

Warm-Up: December 15, 2011. Divide and express the result in standard form. Homework Questions?. Quadratic Functions. Section 2.2. Quadratic Functions. A quadratic function is any function that can be written in the form The graph of a quadratic function is a parabola .

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Warm-Up: December 15, 2011

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

  2. Homework Questions?

  3. Quadratic Functions Section 2.2

  4. 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.

  5. Example Graphs Axis of Symmetry Vertex

  6. 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,

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

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

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

  10. 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.

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

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

  13. 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

  14. 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?

  15. 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?

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

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