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Lesson 1-7

Lesson 1-7. Quadratic Functions and Their Graphs. Objective:. Objective:. To define and graph quadratic functions. Quadratic Function:. Quadratic Function:. f(x) = a x 2 + b x + c where a 0. Quadratic Function:. f(x) = a x 2 + b x + c where a 0.

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Lesson 1-7

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  1. Lesson 1-7 Quadratic Functions and Their Graphs

  2. Objective:

  3. Objective: To define and graph quadratic functions.

  4. Quadratic Function:

  5. Quadratic Function: f(x) = ax2 + bx +c where a 0.

  6. Quadratic Function: f(x) = ax2 + bx +c where a 0. The graph of a quadratic function is called a parabola.

  7. Special Parts of a Parabola:

  8. Special Parts of a Parabola: Vertex: The turning point. It is either a maximum or minimum.

  9. Special Parts of a Parabola: Axis of Symmetry: A vertical line that passes through the vertex. http://2012books.lardbucket.org/books/elementary-algebra/section_12_05.html

  10. Special Parts of a Parabola: Axis of Symmetry: This line is midway between the x-intercepts therefore it is the “average” of the x-values. http://2012books.lardbucket.org/books/elementary-algebra/section_12_05.html

  11. Axis of Symmetry:

  12. Axis of Symmetry: Can always be found by calculating the formula

  13. Vertex:

  14. Vertex: Can always be found using the formula

  15. Discriminant:

  16. Discriminant: • If b2 – 4ac > 0 Parabola crosses x-axis twice. There will be two x-intercepts.

  17. Discriminant: • If b2 – 4ac > 0 Parabola crosses x-axis twice. There will be two x-intercepts. • If b2 – 4ac = 0 Parabola is tangent to the x-axis. There is only one x-intercept.

  18. Discriminant: • If b2 – 4ac > 0 Parabola crosses x-axis twice. There will be two x-intercepts. • If b2 – 4ac = 0 Parabola is tangent to the x-axis. There is only one x-intercept. • If b2 – 4ac < 0 Parabola never crosses the x-axis so there are no x-intercepts.

  19. Find the intercepts, axis of symmetry, and the vertex of the given parabola.y = (x + 4)(2x – 3)

  20. Now sketch the graph.

  21. Sketch the graph of the parabola. Label the intercepts, the axis of symmetry, and the vertex.y = 2x2 – 8x + 5

  22. If the equation can be written in the form of :

  23. If the equation can be written in the form of : then the vertex of the parabola is (h, k) and the axis of symmetry is the equation x = h.

  24. Find the vertex of the parabola by completing the square.y = -2x2 + 12x + 4

  25. Now, find the x- and y-intercepts.y = -2x2 + 12x + 4

  26. Find the equation of the quadratic function f with f(-1) = -7 and a maximum value f(2) = -1. Show that the function has no x-intercepts.

  27. Where does the line y = 2x + 5 intersect the parabola y = 8 – x2?*Show this both algebraically and graphically.

  28. Find an equation of the function whose graph is a parabola with x-intercepts 1 and 4 and a y-intercept of -8.

  29. Assignment:Pgs. 40-41C.E. 1-6 allW.E. 1-25 (Left Column)

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