1. Working With Quadratics M 110 Modeling with Elementary Functions Section 2.1 Quadratic Functions V. J. Motto

2. The Quadratic Function General Form: y = ax 2 + bx + c Vertex Form: y = a(x – h) 2 + k

3. Graphing - 1 Graphing Need at least 3 points to sketch the graph If a > 0, the parabola opens upward If a <0, the parabola opens downward. Important points are: y-intercept vertex x-intercepts or zeros or roots

4. General Form: y = ax 2 + bx + c Finding points to graph: y-intercept is ( 0, c) The vertex The x-coordinate is give by. Use your calculator to find the y-coordinate. Use the formula:

5. General Form: y = ax 2 + bx + c Finding points to graph: x-intercept or zeros Use your calculator: 2 nd +Trace, option 2:zeros. You will need to declare a left bound and right bound. You need to search for each x-intercept separately.

6. General Form: y = ax 2 + bx + c Finding points to graph: x-intercept or zeros (continued) Since the y-coordinate of an x-intercept is always 0. You need to solve the equation: 0 = ax 2 + bx + c. Techniques Factoring Quadratic Formula:

7. Vertex Form: y = a(x – h) 2 + k The vertex is ( h, k). The search for the other point is often done by converting the vertex form to the general form.

8. Example 1 - Graph y = 2x 2 + 4x - 6

9. Example 2 – Solve the following a. -x 2 + 6x – 6 = 0 b. -x 2 + 6x – 9 = 0 c. -x 2 + 6x – 12 = 0

10. Example 3: Complete the following table for the function y = 2x 2 + 4x - 6. x7- 12 y159