1. 5.2.1 – Vertex and Intercept Form

2. Standard form is just one version to express a quadratic Tricky to use because we always must use the vertex formula Two alternative ways to also write the form of a quadratic

3. Vertex Form Vertex Form; y = a(x – h) 2 + k, where (h, k) is the vertex – If a > 0, opens up (vertex is a minimum) – If a < 0, opens down (vertex is a maximum) Convenient since we now can find the vertex without having to use tricky formula Still graph by finding a second point and using the concept of symmetry

4. Example. Find the vertex from the following quadratics: 1) y = 2(x – 5) 2 + 4 2) y = -5(x + 2) 2 – 10 3) y = (x + 1) 2 + 9 4) y = 3x 2 + 7.9 5) y = (x – π) 2

5. Example. Graph the following quadratic. y = -2(x – 2) 2 + 1 Up or down? Vertex? Second point?

6. Example. Graph the following quadratic. y = (x – 3) 2 - 1 Up or down? Vertex? Second point?

7. Example. Graph the following quadratic. y = -(x – 2) 2 + 3 Up or down? Vertex? Second point?

8. Remember, we can still use our calculators as well to plot these, regardless what form Example. Using your calculator, plot the following function and determine the vertex. y = 4(x + 3) 2 - 1

9. Application In terms of a parabola, we can fit the model to the path objects sometimes travel Using our calculators, we can determine info such as the maximum height

10. Example. The leap of a dolphin out of water is given by the function y = -0.03(x – 14) 2 + 9. Determine the following: A) sketch the graph of the jump B) Find the maximum height of the jump

11. Assignment Pg. 231 4-6, 10-12, 23-27 odd, 35-39 (may use your calculator)