1 / 12

4-2 Translating Parabolas

4-2 Translating Parabolas. Warm-up What is the coefficient of x 2 in the function The vertex of a parabola is at (2, -7). If the parabola is translated 5 units to the right and 6 units down, what are the coordinates of the new vertex? Find the value of 2 x 2 when x = -1.

nero
Télécharger la présentation

4-2 Translating Parabolas

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. 4-2 Translating Parabolas Warm-up • What is the coefficient of x2 in the function • The vertex of a parabola is at (2, -7). If the parabola is translated 5 units to the right and 6 units down, what are the coordinates of the new vertex? • Find the value of 2x2 when x = -1. • Rewrite 2(x + 5)2 + 6 as a sum of three terms. • If • –3 • (7, -13) • 2 • 2x2 + 20x + 56 • y =-2 Integrated 2 4-1 Graphing Quadratic Functions

  2. 4-1 Graphing Quadratic Functions Today we will: • Explore translations of parabolas. Tomorrow we will: • Solve quadratic equations by graphing and undoing. Integrated 2 4-1 Graphing Quadratic Functions

  3. Width of Parabola • The value of a in the function affects the width of the graph. • The greater the absolute value of a, the narrower the graph. Integrated 2 4-1 Graphing Quadratic Functions

  4. Example 1 Tell whether the graph of each function is wider than, narrower than, or the same shape as the graph of y = x2. • Solution • The value of a is –3. Since |-3| > 1, the graph is narrower than the graph of y = x2. • In standard form, this function is . The value of a is –1. Since |-1| = 1, this graph has the same shape as the graph y = x2. • The value of a is 2/3. Since | 2/3 | < 1, this graph is wider than the graph of y = x2. Integrated 2 4-1 Graphing Quadratic Functions

  5. Example 2 Arrange these quadratic functions in order from the one with the narrowest graph to the one with the widest graph. Solution Integrated 2 4-1 Graphing Quadratic Functions

  6. Translations • The graph of is a translation of the graph . • A translation changes only the position of a graph; • it doesn’t change the size or shape of the graph, or • the direction that the graph opens. Integrated 2 4-1 Graphing Quadratic Functions

  7. Translations Subtraction indicates a translation to the right. Addition indicates a translation to the left. Translations can also occur in two directions at the same time. A graph can be translated to the right and up, to the right and down, to the left and up, and to the left and down. Integrated 2 4-1 Graphing Quadratic Functions

  8. Solution: • To translate the graph of 3 units to the right, replace x with (x-3). • To translate the graph of down 5 units, subtract 5 from . • The equation of the parabola is Example 3 Give the equation of the parabola that results when the graph of is translated 5 units down and 3 units to the right. Integrated 2 4-1 Graphing Quadratic Functions

  9. Solution: • To translate the graph of 7 units to the left replace x with (x+7). • To translate the graph of up 1 unit, add 1 to . Example 4 Give the equation of the parabola that results when the graph of is translated 7 units to the left and 1 unit up. Integrated 2 4-1 Graphing Quadratic Functions

  10. Example 5 Tell how to translate the graph of in order to produce the graph of each function. Translate 9 units left Translate 9 units up Translate 2 units right and 1 unit up Translate 12 units right and 3 units down Integrated 2 4-1 Graphing Quadratic Functions

  11. Find the coordinates of the vertex of the graph of Solution The graph of is a translation of the graph 6 units left and 8 units up. The vertex of the graph of is 6 units to the left and 8 units up from the vertex of the graph of , which is (0, 0). (0 – 6, 0 + 8) (-6, 8) Example 6 The coordinates of the vertex are (-6, 8) Integrated 2 4-1 Graphing Quadratic Functions

  12. Table of Quadratic Formulas Integrated 2 4-1 Graphing Quadratic Functions

More Related