1. 5-3 Using Transformations to Graph Quadratic Functions

2. Warm Up For each translation of the point (–2, 5), give the coordinates of the translated point. 1. 6 units down 2. 3 units right (–2, –1) (1, 5) For each function, evaluate f(–2), f(0), and f(3). 3. f(x) = x 2 + 2x + 6 4. f(x) = 2x 2 – 5x + 1 6; 6; 21 19; 1; 4 Bell Ringer

3. What is a Quadratic Function?

4. The vertex of the parabola is at (h, k).

5. Vertex form of a quadratic can be used to determine transformations of the quadratic parent function. Quadratic parent function: f(x) = x 2 x y=f(x) -24 1 00 11 24 39

6. Horizontal Translations: If f(x) = (x – 2) 2 then for (x – h) 2,(x – (2)) 2, h = 2. The graph moves two units to the right. f(x) =x 2 f(x) = (x – 2) 2

7. Horizontal Translations: If f(x) = (x + 3) 2 then for (x – h) 2,(x – (-3)) 2, h = -3 The graph moves three units to the left. f(x) =x 2 f(x) = (x + 3) 2

8. Vertical Translations: If f(x) = (x) 2 + 2 then for (x – h) 2 + k, (x) 2 + 2, k = 2 The graph moves two units up. f(x) =x 2 f(x) = (x) 2 + 2

9. Vertical Translations: If f(x) = (x) 2 – 1 then for (x – h) 2 + k, (x) 2 – 1, k = -1 The graph moves one unit down. f(x) =x 2 f(x) = (x) 2 – 1

10. Horizontal and Vertical Translations: If f(x) = (x – 3) 2 + 1 then for (x – h) 2 + k, (x – (3)) 2 + 1, h = 3 and k = 1 The graph moves three units right and 1 unit up. f(x) =x 2 f(x) = (x – 3) 2 + 1

11. Horizontal and Vertical Translations: If f(x) = (x + 1) 2 – 2 then for (x – h) 2 + k, (x – (-1)) 2 – 2, h = -1 k = -2 The graph moves one unit left and two units down. f(x) =x 2 f(x) = (x + 1) 2 – 2

12. Reflection: If a is positive, the graph opens up. If a is negative, the graph is reflected over the x-axis.

13. Vertical Stretch/Compression: The value of a is not in the parenthesis: a(x) 2. If |a| > 1, the graph stretches vertically away from the x-axis. If 0 < |a| < 1, the graph compresses vertically toward the x-axis. f(x) = 2x 2, a = 2, stretch vertically by factor of 2. f(x) =x 2 f(x) = 2x 2

14. f(x) =x 2

16. f(x) =x 2 f(x) =(2x) 2

17. Vertical Stretch: f(x) = 2x 2 xf(x) 12(1) 2 = 2 22(2) 2 = 8 32(3) 2 = 18 xf(x) 1 2 3 x 1 2 3 Hor. Compress: f(x) = (2x) 2 xf(x) 1(2∙1) 2 =4 2(2∙2) 2 = 16 3(2∙3) 2 =81 a = 2