1.  How would you sketch the following graph? ◦ y = 2(x – 3) 2 – 8  You need to perform transformations to the graph of y = x 2  Take it one step at a time

2.  y = 2(x – 3) 2 – 8 – Let’s start with the 2 infront  y = 2x 2 means that the graph becomes vertically stretched/ horizontally compressed  y = 2(x – 3) 2 – 8 – Now let’s deal with the -3  This gets subtracted from the x  y = 2(x – 3) 2 means that the graph gets translated horizontally 3 units to the right  y = 2(x – 3) 2 – 8 – Now let’s deal with the -8  This “-8” means that the function gets translated vertically 8 units down

3. y = x 2 y = 2x 2 y = 2(x-3) 2

4. y = 2(x-3) 2 - 8

5.  Compared to the graph of y = x 2, the graph of y = a(x – h) 2 + k is a parabola that is: ◦ Stretched/compressed vertically by a factor “a” ◦ Translated horizontally by “h” ◦ Translated vertically by “k” ◦ Also, if a < 0, parabola is reflected in the x-axis  The vertex of y = a(x – h) 2 + k is (h, k)