Chapter 10-5 Lines X Lines

A quadratic function can be considered to be the product of two linear functions - so a parabola can be thought of as the result of multiplying two lines together. What would be the effect on the parabola when either linear factor is changed.

In this Interactive Diagram, only the straight lines can be changed. You can drag a line to translate it. You can also pivot a line by grabbing one of its ends. And, if you want to change the pivot point of a line, drag the triangle to the right or left. The pivots (or fulcrums) of the lines can be very handy.

Questions
1. In a parabola that is the product of two linear functions, what changes in the parabola's equation if you alter the slopes of the lines? What changes if you change the lines' y-intercepts? If both linear factors are identical, how many solutions are possible for the equation below?

0 = ax² + bx + c

2. Match three different parabolas by changing only their linear function factors. For each one: Press the "Graph Target" button and match the curve that appears. (And read question 3...)

3. When you generated parabolas to match, did you get any you could not match by changing the lines? Explain why you could not match it.