1. Quadratic Function Finding the Solutions (roots) of a Quadratic Function by Graphing

2. Quadratic Function (y = ax 2 + bx + c) a, b, and c are called the coefficients. The graph will form a parabola. Each graph will have either a maximum or minimum point. There is a line of symmetry which will divide the graph into two halves.

3. y = x 2 a = 1, b = 0, c = 0 Minimum point (0,0) Axis of symmetry x=0 y=x 2

4. What happen if we change the value of a and c ? y=3x 2 y=-3x 2 y=4x 2 +3 y=-4x 2 -2

5. Conclusion (y = ax 2 +bx+c) When a is positive, When a is negative, When c is positive When c is negative the graph opens upward. the graph opens downward. the graph moves up. the graph moves down.

6. What happens if b varies? Explore – Axis of Symmetry x=-b/2a The ‘b’ moves the AOS left/right

7. Solving Quadratic Functions (ax 2 + bx + c = 0) Since y = ax 2 + bx +c, by setting y=0 we set up a quadratic equation. To find the solutions means we need to find the x-intercept. Since the graph is a parabola, there will be two solutions.

8. To solve quadratic equations (graphing method) X 2 - 2x = 0 To solve the equation, put y = x 2 -x into your calculator. Find the x intercept. Two solutions, x=0 and x=2. y=x 2 -2x

9. Find the Solutions y=x 2 -4 y=x 2 +2x-15 y=-x 2 +5y=-x 2 -1

10. Find the solutions y=x 2 +2x+1 y=-x 2 +4x-1

11. Observations Sometimes there are two solutions. Sometimes there is only one solution. Sometimes it is hard to locate the solutions. Sometimes there is no solution at all.

12. Other Methods By factoring By using the quadratic formula

13. The End