**Problem 3**

Review of
*solve*
and
*subs*
from the previous class.

As part of the homework you completed for Mathematics with Maple Workshop 3, you did the following problem. (If you haven't done the problem, do it now. If you don't know how to do the problem, get help.)

*Problem from homework: *
The general equation for a parabola with a vertical axis of symmetry is
.

(a) Find the equation of such a parabola that passes through the points (0,5), (4,6), and (5,10).

(b) Estimate (by plotting) the y-value of the lowest point on the graph of this parabola.

(Note: the
*MapleIntro3 *
worksheet gave some hints for solving this problem.)

In that exercise, you found the equation of a parabola through three specific points. In this problem you should generalize that to get the equation of the parabola through three
__general__
points.

(a) Find a formula for the equation of the parabola
that passes through
*(x1, y1)*
,
*(x2, y2)*
, and
*(x3, y3)*
. You should be able to do this by going through the same steps that you did in that example.

(b) Apply the general formula from part (a) to the points (0,5), (4,6), and (5,10) by using
*subs*
to substitute these points into the general formula. Now you can surely see the benefits of the
*subs*
command --- you would never want to have to plug in these numbers by hand for all the
*x1*
's,
*x2*
's, etc.

(c) Using your general formula (and
*subs*
of course!), plot the graph of the parabola that goes through the three points (2,4), (3,8), and (7,-1). Use the
*plot*
command to also plot the three points themselves, and overlay this plot onto the parabola plot (use
*display*
), so that we can see the points and parabola on the same plot.