1 / 19

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

Download Presentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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:

More Related