1. Table of Contents Graphing Quadratic Functions – Concept A simple quadratic function is given by The graph of a quadratic function in called a parabola. Here is the graph of a very basic quadratic function:

2. Table of Contents The value of the coefficient a determines the direction the parabola faces. When a is positive, the parabola faces up. When a is negative, the parabola faces down.

3. Table of Contents Example 1 Face Up Face Down

4. Table of Contents The vertex of a parabola is the lowest point (minimum y-value) on the graph of a parabola … Vertex Minimum Maximum … or the highest point (maximum y-value) on the graph.

5. Table of Contents The axis of symmetry of a parabola is the vertical line going through the vertex. Notice the symmetry of the two branches of the parabola about the axis. Example 2 Draw the axis through the vertex.

6. Table of Contents The equation of the axis of symmetry is given by In this case, the equation of the axis of symmetry is given by:

7. Table of Contents When graphing quadratic functions, it can be helpful to plot all intercepts. x-interceptsy-intercepts Set y = f (x) = 0 and solve for x. Set x = 0 and solve for y. This is where the graph intersects the x-axis. This is where the graph intersects the y-axis.

8. Table of Contents x-intercepts Example 3 y-intercept

9. Table of Contents SUMMARY Axis of symmetry: Graphs of Quadratic Functions The graph of a quadratic function in called a parabola. The maximum or minimum y-value of a quadratic occurs at the vertex. Face UpFace Down x-int: y = f (x) = 0 and solve for x. y-int: x = 0 and solve for y.

10. Table of Contents