C. Analyzing Quadratic Functions Expressed in Factored Form

In the previous section, you saw that changing a, b, and c in changed the shape, location, and/or orientation of the graph. However, you also saw what limited information is readily available from this form. Rewriting the function in different forms makes additional information more readily available.

In this section, you will discover how the x-intercepts of the graph of a quadratic function can easily be determined when the function is expressed in factored form.

In the Warm Up you reviewed factoring by identifying greatest common factors and by decomposing trinomials. Those factoring techniques will be used here.

Example 1

Write in factored form.

Step 1: Identify the greatest common factor of all three terms.

GCF = −2

Step 2: Factor .

Determine two numbers that multiply to −20 and add to 1. The values −4 and 5 will work.

Step 3: Combine this with the GCF of −2 you found earlier to write the function in factored form.