Graphing Quadratic Functions Standard Form It is assumed

Graphing Quadratic Functions – Standard Form • It is assumed that you have already viewed the previous slide show titled Graphing Quadratic Functions – Concept. • A quadratic function in what we will call Standard Form is given by: • The summary of the Concept slide show is given again on the next page.

SUMMARY Face Up Face Down Narrow Wide Vertex Axis of symmetry

• One more thing is needed before sketching the graph of a quadratic function. A point is plotted to know just how narrow or how wide the graph is. • When the graph is narrow, choose an x-value that is only one unit from the vertex. • In the graph on the right, a good choice would be x=1 Narrow

• If the value x = 2 were chosen, then the corresponding y-value would be off the graph.

• When the graph is wide, choose an x-value that is more than one unit from the vertex. • In the graph on the right, a good choice would be x = 2 or x = 3 • Note that x = 1 would not be very helpful in determining just how wide the graph would be. Wide

SUMMARY Narrow Choose a value for x 1 unit away from the vertex. Wide Choose a value for x more than 1 unit away from the vertex

• Example 1: Sketch the graph of the following function:

• Plot the vertex: • Draw the axis of symmetry:

• Since the graph is narrow, find a point that is only 1 unit from the vertex. Try x = 3.

• Draw the right branch of the parabola using the vertex and the point (3, 4). • Now use symmetry to draw the left branch. • Label the axis and important points.

• Example 2: Sketch the graph of the following function: Face Down Vertex: Wide Axis:

• Plot the vertex: • Draw the axis of symmetry:

• Since the graph is wide, find a point that is more than 1 unit from the vertex (-1, -2). • This problem presents another challenge, which is to avoid fractions if possible.

• Therefore, we want to meet two goals: 1. Select an x-value more than one unit to the right of the vertex (-1, -2). 2. Avoid fractions. • To meet goal #2, all that is needed is for the quantity that is squared to be divisible by 5. • An x-value of 4 meets this condition, and also satisfies goal #1.

• Draw the right branch of the parabola using the vertex and the point (4, -7). • Now use symmetry to draw the left branch. • Label the axis and important points.