1 / 10

§9.2 Quadratic Functions

§9.2 Quadratic Functions. Evaluate the expression for the following values of a and b . a = –6, b = 4 2. a = 15, b = 20 Graph each function. 5 . y = x 2 6. y = – x 2 + 2 . – b 2 a. Warm-Up. 1 3. for a = –6, b = 4. for a = 15, b = 20. =. =. –4 –12. –20

doyle
Download Presentation

§9.2 Quadratic Functions

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. §9.2 Quadratic Functions

  2. Evaluate the expression for the following values of a and b. a= –6, b = 4 2.a= 15, b = 20 Graph each function. 5.y = x26. y= –x2 + 2 –b 2a Warm-Up

  3. 1 3 for a = –6, b = 4 for a = 15, b = 20 = = –4 –12 –20 30 –4 2(–6) –20 2(15) 5. y = x2 6. y = –x2 + 2 b 2a b 2a – 1. – 2 3 – = = 2. Solutions

  4. Property Graph of a Quadratic Function The graph of y = ax2 + bx + c, where a ≠ 0, has the line x = -b/2a as its axis of symmetry. The x-coord. of the vertex is –b/2a.

  5. Step 1: Find the equation of the axis of symmetry and the coordinates of the vertex. Find the equation of the axis of symmetry. x = = = – 1 The x-coordinate of the vertex is –1. b 2a y = 2x2 + 4x – 3 y = 2(–1)2 + 4(–1) – 3 = –5 – To find the y-coordinate of the vertex, substitute –1 for x. –4 2(2) The vertex is (–1, –5). Example 1: Graphing y = ax2 + bx + c Graph the function y = 2x2 + 4x – 3.

  6. Choose a value for x on the same side of the vertex. Let x = 1 y = 2(1)2 + 4(1) – 3   = 3 For x = 1, y = 3, so another point is (1, 3). Find the y-coordinate for x = 1. Example 1: Graphing y = ax2 + bx + c (continued) Step 2: Find two other points. Use the y-intercept. For x = 0, y = –3, so one point is (0, –3).

  7. Then draw the parabola. Example 1: Graphing y = ax2 + bx + c (continued) Step 3:Reflect (0, –3) and (1, 3) across the axis of symmetry to get two more points.

  8. Example 2: Using the Vertical Motion Model Aerial fireworks carry “stars,” which are made of a sparkler-like material, upward, ignite them, and project them into the air in fireworks displays. Suppose a particular star is projected from an aerial firework at a starting height of 610 ft with an initial upward velocity of 88 ft/s. How long will it take for the star to reach its maximum height? How far above the ground will it be? The equation h = –16t2 + 88t + 610 gives the height of the star h in feet at time t in seconds. Since the coefficient of t2 is negative, the curve opens downward, and the vertex is the maximum point.

  9. – b 2a Step 1: Find the x-coordinate of the vertex. After 2.75 seconds, the star will be at its greatest height. –88 2(–16) = = 2.75 Example 2: Using the Vertical Motion Model (continued) Step 2:  Find the h-coordinate of the vertex. h = –16(2.75)2 + 88(2.75) + 610 Substitute 2.75 for t. h = 731 Simplify using a calculator. The maximum height of the star will be about 731 ft.

  10. Assignment: Pg. 556-558 8, 9, 11, 12, 14, 15, 17-19, 21, 22, 24, 25, 28-35

More Related