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:

The value of the coefficient a determines 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.

Example 1: Face Up Face Down

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

Example 2: Narrow Wide

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

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:

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

The vertex is given by: 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 …

Example 4: The vertex is given by:

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 5: Draw the axis

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:

SUMMARY Face Up Face Down Narrow Wide Vertex Axis of symmetry