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.
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
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.
4. On this interactive diagram, there are three
different colored regions (green, white, blue). What feature (or features)
of the parabola and the lines determines the location of those colored