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Warm-Up: November 6, 2015

This homework assignment focuses on graphing quadratic functions in standard form and general form. It covers topics such as finding the vertex, intercepts, axis of symmetry, and determining the domain and range of the graph. Examples and practice questions are included.

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Warm-Up: November 6, 2015

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  1. Warm-Up: November 6, 2015 • Divide and express the result in standard form

  2. Homework Questions?

  3. Quadratic Functions(use graph paper or guided notes) 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 an axis of symmetry that intersects the vertex.

  5. Example Graphs Axis of Symmetry Vertex

  6. Standard Form of a Quadratic Function • Vertex is at • Axis of symmetry is the line • If , the parabola is concave up • If , the parabola is concave down

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

  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 • -intercepts can be found by quadratic formula (or sometimes by factoring and zero product property) • -intercept is at • Graph the parabola using these points just as we did before. • Or you can complete the square to get standard form.

  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 , then has a minimum • If , then 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, , in feet, when it is 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, , in feet, 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 • Read Section 2.2 • Page 264 #1-8 ALL (use your graphing calculator for 5-8), #9-41 Every Other Odd

  17. Exercises 1-8 use graphs in book • In Exercises 9-16, find the coordinates of the vertex for the parabola defined by the given quadratic function. • In Exercises 17-34, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola’s axis of symmetry. Use the graph to determine the function’s domain and range.

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