1. 1 Solving Quadratic Equations 1Shaw 2008 February 16, 2010

2. 22Shaw 2008

3. 3 STANDARD FORM: QUADRATIC EQUATION Parabola: The graph of a Quadratic Equation 3Shaw 2008

4. 4 Negative value for a: The Parabola opens DOWN  For example  What is the value for a? It’s a sad graph 4Shaw 2008

5. 5 Positive value for a: The Parabola opens UP  For example  What is the value for a? It’s a happy graph! 5Shaw 2008

6. 6 VERTEX Where would the Vertex be on these two graphs? 6Shaw 2008

7. 7 VERTEX If a is positive: the vertex is the MINIMUM value of the function. If a is negative: the vertex is the MAXIMUM value of the function.  The Vertex always lies on the LINE OF SYMMETRY Shaw 2008

8. 8 EXAMPLE 1 What do we know:  Does this graph open up or down?  Does the vertex have a MAXIMUM or a MINIMUM value? 8Shaw 2008

9. 9 EXAMPLE 2  Does the graph face up or down?  Is the vertex a Max or Min? Shaw 2008

10. Solving Quadratic Equations When you are “solving” a quadratic equation you are finding the x-intercepts of the graph How many solutions will the equation have? Solve the following equation by graphing:

11. Solving Quadratic Equations Solve the following two equations algebraically What variable should we solve for?

12. Solving Quadratic Equations Solve the following equations algebraically

13. 13 HOMEWORK # 14!!! Solving Quadratic Equations Worksheet #3-21 multiples of 3 #52, 53, 55 #24-45 multiples of 3, 44, 47 Shaw 2008