Graphing Quadratic Functions – Concept

1. Graphing Quadratic Functions – Concept • A quadratic function in what we will call Standard Form is given by: • The graph of a quadratic function is called a parabola. Here is the graph of a very simple quadratic function:

2. The value of the coefficient adetermines the direction the parabola faces. • When the value of a is positive, the parabola faces up. • When the value of a is negative, the parabola faces down.

3. Example 1: Face Down Face Up

4. The value of the coefficient aalso determines the shape of the parabola. • When |a| > 1 the parabola is narrow. • When 0 < |a| < 1 the parabola is wide.

5. Example 2: Wide Narrow

6. Vertex Vertex • The vertex of a parabola is the highest point or the lowest point on the graph of a parabola.

7. The vertex of a parabola whose function is given in standard form … … is given by V(h,k). • Example 3: The vertex is given by:

8. Example 3: Put the function in the form of … The vertex is given by:

9. Here is an easier way to work the last problem: For the h value, take the opposite sign … For the k value, take the same sign … The vertex is given by:

10. Example 4: The vertex is given by:

11. The axis of symmetry of a parabola is the vertical line going through the vertex. • Example 5: Draw the axis Notice the symmetry of the two branches of the parabola about the axis.

12. The equation of the axis of symmetry is given by where h is the x-value of the vertex. In this case, the equation of the axis of symmetry is given by:

13. SUMMARY Vertex Face Up Face Down Axis of symmetry Narrow Wide

14. END OF PRESENTATION