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Section 9.1

Section 9.1. Graphing Quadratic Functions. Standard 21.0 Students graph quadratic functions and know that their roots are the x -intercepts. Graph quadratic functions. Find the equation of the axis of symmetry and the coordinates of the vertex of a parabola. quadratic function. vertex

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Section 9.1

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  1. Section 9.1 Graphing Quadratic Functions Standard 21.0 Students graph quadratic functions and know that their roots are the x-intercepts.

  2. Graph quadratic functions. • Find the equation of the axis of symmetry and the coordinates of the vertex of a parabola. • quadratic function • vertex • symmetry • axis of symmetry • parabola • minimum • maximum

  3. The graph of a quadratic function is called a parabola. If a is positive, then the parabola opens upward. If a is negative, then the parabola opens downward.

  4. The graph of a quadratic function is called a parabola. If a is positive, then the parabola opens upward. If a is negative, then the parabola opens downward. A wider parabola has a leading coefficient closer to 0. A narrower parabola has a leading coefficient farther from 0. The vertex is the point where the parabola changes direction. It can be either a maximum or a minimum. (x, y) or (h, k)

  5. Graph Opens Upwards Use a table of values to graph y = x2 – x – 2. Graph these ordered pairs and connect them with a smooth curve. Answer: The lowest point of a parabola is called the minimum.

  6. Graph Opens Downward A. ARCHERY The equation y = –x2 + 6x + 4 represents the height y of an arrow x seconds after it is shot into the area. Use a table of values to graph y = –x2 + 6x + 4. Graph these ordered pairs and connect them with a smooth curve. Answer: The highest point of a parabola is called the maximum.

  7. Parabolas have symmetry. • Symmetrical figures are those in which each half of the • figure matches the other exactly. • The line of symmetry cuts a parabola in half. • The equation for the line of symmetry is

  8. Vertex and Axis of Symmetry A. Consider the graph of y = –2x2 – 8x – 2. Write the equation of the axis of symmetry. In y = –2x2 – 8x – 2, a = –2 and b = –8. Equation for the axis of symmetry of a parabola a = –2 and b = –8 Answer: The equation of the axis of symmetry is x = –2.

  9. Vertex and Axis of Symmetry B. Consider the graph of y = –2x2 – 8x – 2. Find the coordinates of the vertex. (x, y) Since the equation of the axis of symmetry is x = –2 and the vertex lies on the axis, the x-coordinate for the vertex is –2. y = –2x2 – 8x – 2 Original equation y = –2(–2)2 – 8(–2) – 2 x = –2 y = –8 + 16 – 2 Simplify. y = 6 Add. Answer: The vertex is (–2, 6).

  10. Vertex and Axis of Symmetry C. Consider the graph of y = –2x2 – 8x – 2. Identify the vertex as a maximum or minimum. Answer: Since the coefficient of the x2 term is negative, the parabola opens downward and the vertex is a maximum point.

  11. A. Consider the graph of y = 3x2 – 6x + 1. Write the equation of the axis of symmetry. A.x = –6 B.x = 6 C.x = –1 D.x = 1

  12. B. Consider the graph of y = 3x2 – 6x + 1. Find the coordinates of the vertex. A. (–1, 10) B. (1, –2) C. (0, 1) D. (–1, –8)

  13. C. Consider the graph of y = 3x2 – 6x + 1. Identify the vertex as a maximum or minimum. A. minimum B. maximum C. neither D. cannot be determined

  14. A. B. C.D. D. Consider the graph of y = 3x2 – 6x + 1. Graph the function.

  15. A B C D Match Equations and Graphs Which is the graph of y = –x2 – 2x –2?

  16. Homework Assignment #56 9.1 Skills Practice Sheet

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