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8.3 Graphing Quadratic Functions

8.3 Graphing Quadratic Functions. Algebra 2 Mrs. Spitz Spring 2007. Objectives. Graph quadratic equations of the form y = (x – h) 2 + k, and identify the vertex and the equation of the axis of symmetry of a parabola. Assignment. pp. 363-364 #6-42 all. What do you have to do?.

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8.3 Graphing Quadratic Functions

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  1. 8.3 Graphing Quadratic Functions Algebra 2 Mrs. Spitz Spring 2007

  2. Objectives • Graph quadratic equations of the form y = (x – h)2 + k, and identify the vertex and the equation of the axis of symmetry of a parabola. Assignment pp. 363-364 #6-42 all

  3. What do you have to do? • I was going to go into a long explanation. However, the long and short of it—here’s what you have to do: • Axis of symmetry • Find the vertex • Choose 5 points to graph the parabola • Write the equation

  4. Ex. 1: Name the vertex and axis of symmetry for the graph of each equation. y = (x + 8)2 – 1 . How is this graph different from y = x2 Remember the format. y = (x – h)2 + k The vertex is at (h, k), but h is opposite because the negative sign. So, if you look at the equation, the vertex should be at (-8, -1).

  5. Ex. 1: Name the vertex and axis of symmetry for the graph of each equation. y = (x + 8)2 – 1 . How is this graph different from y = x2 The axis of symmetry happens to be whatever the h is in (h, k). So in this case, h = - 8, so x = -8. It differs from the graph y = x2 in that the vertex is translated 8 units to the left and 1 unit down.

  6. Ex. 2: Name the vertex and axis of symmetry for the graph of each equation. Table of values y = (x + 1)2 +3. Then draw the graph. The vertex is (h, k)—opposite h. (-1, 3) The axis of symmetry will be x = -1.

  7. y = (x + 1)2 +3. Then draw the graph. The vertex is (h, k)—opposite h. (-1, 3) The axis of symmetry will be x = -1. Ex. 2: Name the vertex and axis of symmetry for the graph of each equation. Notice that the points with the same y-coordinates are the same distance from the axis of symmetry, x = -1

  8. Ex. 3: Write the equation of the quadratic function for each graph. The vertex of this parabola is at (-2, 0) which is (h, k) y = (x – h)2 + k, y = (x – (-2))2 + 0 y = (x + 2)2 + 0

  9. Ex. 4: Write each equation in the form y = (x – h)2 + k. Then name the vertex and the axis of symmetry. 19. f(x)= x2 – 4x +4 (You have to factor. If you can’t recognize this yet, you are in trouble.) y = (x – 2)2 + 0 The vertex is at (2, 0) and the axis of symmetry is at x = 2

  10. Ex. 5: Write each equation in the form y = (x – h)2 + k. Then name the vertex and the axis of symmetry. • f(x)= x2 – 7 y = (x – 0)2 – 7 The vertex is at (0, -7) and the axis of symmetry is at x = 0

  11. What do you have to do? • Problems #27-42, you have to graph. You need the following: • Write the equation • Axis of symmetry • Find the vertex • Choose 5 points to graph the parabola • Graph the parabola

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