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Section 5-2: Graphing Quadratic Functions in Vertex or intercept form

Section 5-2: Graphing Quadratic Functions in Vertex or intercept form. Goal: Graph quadratic functions in different forms. Warm-ups. Find the product: (x + 6)(x + 3) (x – 5) 2 4(x + 5)(x – 5) Write y = x(8x + 12) + 5 in Standard form. Vertex form. y = a(x – h) 2 + k

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Section 5-2: Graphing Quadratic Functions in Vertex or intercept form

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  1. Section 5-2: Graphing Quadratic Functions in Vertex or intercept form Goal: Graph quadratic functions in different forms

  2. Warm-ups • Find the product: • (x + 6)(x + 3) • (x – 5)2 • 4(x + 5)(x – 5) • Write y = x(8x + 12) + 5 in Standard form

  3. Vertex form • y = a(x – h)2 + k • When a>0 the parabola opens up • When a<0 the parabola opens down • Step 1:Draw the axis of symmetry. It is the line x = h. • Step 2: Plot the vertex (h, k) • Step 3:Plot two points on one side of the axis of symmetry. Use symmetry to plot two more points on the opposite side of the axis of symmetry • Step 4: Draw a parabola through the points Definition Steps to Graphing

  4. Example 1: Graph y = -2(x – 2)2 + 1

  5. Additional Example: Graph y = ½ (x – 3)2 - 5

  6. Intercept form • y = a(x – p)(x – q) • When a < 0 the parabola opens down • When a > 0 the parabola opens up • The graph will contain (p , 0) and (q , 0) • Step 1: Draw the axis of symmetry. It is the line x = p + q 2 • Step 2: Find and plot the vertex. The x-coordinate of the vertex is p + q 2 Substitute the x-coordinate for x in the function to find the y-coordinate of the vertex. • Step 3: Plot the points where the x-intercepts, p and q, occur. • Step 4: Draw a parabola Definition Steps for Graphing

  7. Example 2: Graph y = (x + 1)(x + 3)

  8. Additional Example: Graph y = (x + 2)(x - 4)

  9. Checkpoint:Graph y = (x – 3)2 - 1

  10. Checkpoint:Graph y = -(x – 2)2 + 3

  11. Checkpoint:Graph y = 2(x + 1)2 + 4

  12. Checkpoint:Graph y = (x – 3)(x – 7)

  13. Checkpoint:Graph y = -(x – 2)(x – 5)

  14. Checkpoint:Graph y = 2(x + 1)(x – 3)

  15. Minimum and maximum values • Minimum Value • When a > 0 • Maximum Value • When a < 0

  16. Example 3: find the minimum and maximum value • Tell whether the function y = -4 (x + 6)(x – 4) has a minimum value or a maximum value. Then find the minimum or maximum value.

  17. Example 3: find the minimum and maximum value • Tell whether the function y = ½ (x + 8)2 – 12 has a minimum value or a maximum value. Then find the minimum or maximum value.

  18. Example 3: find the minimum and maximum value • Tell whether the function y = 3(x – 4)(x – 7) has a minimum value or a maximum value. Then find the minimum or maximum value.

  19. Homework:

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