2. This is the parent graph of all quadratic functions. The graph of a quadratic function is called a parabola. The parent function is given as

3. A table of values can be constructed from the graph as given to the right. xy xy -39 -24 -11 00 00 11 11 24 24 39 39 (-3,9) (-2,4) (-1,1) (0,0) (1,1) (2,4) (3,9)

4. (-3,9) (-2,4) (-1,1) (0,0) (1,1) (2,4) (3,9) All other quadratic functions can be expressed in the form: This is called the standard form. The general form is given as:

5. In standard form, (h,k) identifies the vertex of the parabola. hk (h,k)

6. In standard form, a affects the direction the parabola opens and how wide or narrow it will open. a Since a=2 and it is positive, the parabola opens up and the y-values are all 2 times larger than on the parent graph. (1,8) (2,2) (3,0) (4,2) (5,8) 2

7. In standard form, If a is negative, the parabola will open down. a Since a=-2 and it is negative, the parabola opens down and the y-values are all 2 times larger than on the parent graph. (1,-8) (2,-2) (3,0) (4,-2) (5,-8) - 2

8. The points where the parabola intersects the x- axis are called the Roots or Zeros of the function. These roots occur when the y-value is equal to zero. Solving for x we get the values: (1,0) (2,6) (3,8) (4,6) (5,0) X= 15 15 1515 1 5 1 5 15 5 1

9. Example:Graph The vertex is (5, -2) The graph opens upward because 3 is positive. The y-values are multiplied by 3. (5, -2) Over 1 up 3

10. The zeros of the function can be found by setting y=0. Now solve for x. The roots or zeros are: (4.33, 0) and (5.66,0)