1. Friday, March 21, 2013 Do Now: factor each polynomial 1)2)3)

2. Questions from Homework?

3. 6-2 Solving Quadratic Equations by Graphing Objectives: Students will be able to 1)Solve quadratic equations by graphing 2)Estimate solutions of quadratic equations by graphing

4. A quadratic equation is an equation in the form: The solution(s) of a quadratic equation are called the roots of the equation. One way to find the roots is to find the zeros of the related quadratic function. The zeros of the function are the x-intercepts of the graph.

5. Take a look at this graph. What are the zeros?

6. The number of solutions depends on how many times the graph crosses the x-axis.

7. Example 1: Solve each equation by graphing. 1)

8. 2)

9. 3)

10. 6-6 Analyzing Graphs of Quadratic Functions Objective

11. Up until this point, when we graphed a quadratic function we needed to put it in standard form, which looked like: Another form that a quadratic function can be written in is vertex form. This looks like:

12. The vertex of the function is the ordered pair (h, k). Note that in vertex form, h is negative. Therefore, when stating the ordered pair of the vertex, h will be the opposite sign of what it is in the function. The axis of symmetry is the line x=h. When a is positive, the parabola opens upwards, and when a is negative, the parabola opens downwards.

13. The parent graph of a parabola is the equation: Just like when we examined absolute value functions in Chapter 2, the graph of a parabola will translate based on certain values being added, subtracted, or multiplied to our parent graph.

14. The k value on the outside of the parenthesis: If k is positive, the graph moves up If k is negative, the graph moves down The h value on the inside of the parenthesis: The a value being multiplied to the function:

16. Example 1: For each quadratic function, identify the vertex, axis of symmetry, and direction of opening. Then, graph the function. 1)

17. 2)

18. Try these. 3)4)