1. Sec. 5-3: Translating Parabolas

2. We will write equations of parabolas using the VERTEX FORM when given the VERTEX and one other point: Y = a(x – h) 2 + k Plug in the point (x, y) and the vertex (h, k) and solve the above equation for a. Finally, rewrite the equation substituting the vertex and “a” values only.

3. Write the vertex form for the parabola that has a vertex of (-2, -6) and contains the point (1, 3). (h, k) (x, y) (-2, -6)(1, 3) Y = a(x-h) 2 + k 3 = a(1 + 2) 2 - 6 3 = a(3) 2 - 6 3 = 9a - 6 9 = 9a so a = 1 Now, plug a, h, & k into the vertex form equation. Y = (x + 2) 2 - 6

4. We can also graph parabolas fairly quickly using the vertex form. Again, just like the old absolute value problems, we identify the VERTEX first and then pick points to the right & left of the vertex to get 2 other points. Graph: Y = (x + 2) 2 - 6 X y V: -2 -6 L: R:

5. Let’s put what we’ve learned all together… Find the equation of a parabola containing the point (-3, 5) and having the vertex (-2,-4) Graph your equation. (x, y) = (-3, 5)(h, k) = (-2, -4) Y = a(x – h) 2 + k