2. Quadratic Functions Solving by Graphing

3. Quadratic Function Standard Form: f(x) = ax 2 + bx + c

4. Solving Quadratic Equations To solve, we need to find the value of x when y = 0 or f(x) = 0. Located at: x-intercepts Referred to as: solutions, zeros, or roots.

5. The number of real solutions is at most two. Quadratic Solutions No Real SolutionsOne SolutionTwo Solutions

6. Example f(x) = x 2 - 4 Identifying Solutions Solutions are x = -2 and x = 2.

7. Quadratic Function (y = ax 2 + bx + c) Each will have a vertex: either a maximum or minimum point. Line of symmetry: divides the graph in two halves

8. Quadratic Functions The graph of a quadratic function is a: If the parabola opens up, the lowest point is called the vertex (minimum). If the parabola opens down, the vertex is the highest point (maximum). Vertex parabola

9. y x Axis of Symmetry Parabolas are symmetric. Axis of symmetry The Axis of symmetry ALWAYS passes through the vertex.

10. Parent Function: f(x) = x 2 a = 1, b = 0, c = 0 Minimum point (0,0) Axis of symmetry x=0 y=x 2

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

12. Conclusion (y = ax 2 +bx+c) When a is positiveConcave (opens up) When a is negative,Convex (opens down) When c is positive, Moves Up When c is negative,Moves Down

13. y = ax 2 + bx + c a > 0 a < 0

14. Finding the Axis of Symmetry When a quadratic function is in standard form the equation of the Axis of symmetry is y = ax 2 + bx + c,

15. STEP 1: Find the Axis of symmetry STEP 2: Make a table of 3 points Axis of Symmetry: Vertex: Min or Max? Roots: Y-intercept:

16. Axis of Symmetry: Vertex: Min or Max? Roots: Y-intercept: