8.4 Notes

1. 8.4 Notes

2. (Page 462) You know how to translate and reflect graphs on a coordinate plane. Now let’s see how to change their shapes. Figures can be stretched or shrunk.

3. Find the vertices of the quadrilateral. Multiply the x-coordinates by 2 and write the image’s vertices in the table provided. Graph the image on the same coordinate plane as the original. What happened to the image? – 6 0 – 4 2 2 3 4 -1 – 3 0 – 2 2 1 3 2 -1 The graph stretched horizontally but stayed the same vertically. (x, y) and (2x, y)

4. Find the vertices of the quadrilateral. Multiply the x-coordinates by 0.5 and write the image’s vertices in the table provided. Graph the image on the same coordinate plane as the original. What happened to the image? – 3 0 – 2 2 1 3 2 -1 – 1.5 0 – 1 2 0.5 3 1 -1 The graph shrunk horizontally but stayed the same vertically. (x, y) (0.5x, y)

5. Find the vertices of the quadrilateral. Multiply the x-coordinates by – 3 and write the image’s vertices in the table provided. Graph the image on the same coordinate plane as the original. What happened to the image? – 3 0 – 2 2 1 3 2 -1 9 0 6 2 -3 3 -6 1 The graph reflected across the y-axis and stretched horizontally but stayed the same vertically. (x, y) and (-3x, y)

6. Find the vertices of the quadrilateral. Multiply the y-coordinates by 2 and write the image’s vertices in the table provided. Graph the image on the same coordinate plane as the original. What happened to the image? – 3 0 – 2 2 1 3 2 -1 – 3 0 – 2 4 1 6 2 -2 The graph stretched vertically but stayed the same horizontally. (x, y) and (x, 2y)

7. Find the vertices of the quadrilateral. Multiply the y-coordinates by 0.5 and write the image’s vertices in the table provided. Graph the image on the same coordinate plane as the original. What happened to the image? – 3 0 – 2 1 1 1.5 2 -0.5 – 3 0 – 2 2 1 3 2 -1 The graph shrunk vertically but stayed the same horizontally. (x, y) and (x, 0.5y)

8. Find the vertices of the quadrilateral. Multiply the x-coordinates by 2 and the y-coordinates by 2 and write the image’s vertices in the table provided. Graph the image on the same coordinate plane as the original. What happened to the image? – 3 0 – 2 2 1 3 2 -1 – 6 0 – 4 4 2 6 4 - 2 The graph stretched vertically and horizontally. (x, y) and (2x, 2y)

9. To vertically stretch or shrink a polygon, you multiply they-coordinates of the vertices by a constant factor. To horizontally stretch or shrink a polygon, you multiply thex-coordinates of the vertices by a constant factor. To vertically stretch or shrink the graph of a function, you again have to multiply the function by a factor. For a function in equation form, y depends upon x, so the stretch or shrink is normally vertically The stretch or shrink factor is usually referred to as a. If 0 <│a│< 1, then the transformation is a shrink If │a│> 1, then the transformation is a stretch **Remember if a is negative the graph is reflected across the x-axis.

10. y = ⅓(x + 6)², shrink by a factor of ⅓ and translation left 6 units Solve for y. Describe the transformation. 3. 3y =( x + 6)² 4. – ⅜ y = │x│ – 6 5. ½ y = (x – 2)² + 3 Reflect across the x-axis, stretch by a factor of 2 ⅔ and translation up 16 units y = 2[(x – 2)²+ 3] y = 2(x – 2)² + 6 Stretched by a factor of 2 and translation right 2 units and up 6 units

11. y = - ¼ [│x + 4│+ 12] y = - ¼ | x+ 4| – 3 Reflected across the x-axis, shrunk by a factor of ¼ , translation left 4 units and down 3 units 6. – 4y = │x + 4│+ 12 7. 8. y = – 2(x – 4)³ – 5 Reflected across the x-axis, stretched by a factor of 3 Reflected across the x-axis, stretched by a factor of 2 , translation right 4 units and down 5 units

12. Find the equation for the function shown in each graph. Graph opens up and is stretched Absolute value Vertex is (2, – 4 ) a= 2 y = 2|x – 2| – 4 Graph opens down and is shrunk Absolute value Vertex is (0, 2) a= ⅓ y = - ⅓|x| + 2

13. Graph opens up and is stretched Absolute value Vertex is (3, – 4 ) a= 2 y = 2(x – 3)² – 4 Graph opens down and is stretched Quadratic function Vertex is (3, – 4 ) a= 2 y = – 2(x – 3)² – 4

14. Graph opens up and is shrunk Quadratic Function Vertex is (3, 4 ) a= 0.5 or ½ y = 0.5 (x – 3)² + 4 Graph opens down and is stretched Absolute value Vertex is ( – 2, – 5 ) a= 3 y = – 3|x + 2| – 5