__March 28, 2007 :: EMAT 6600 :: Problem Solving Class Notes__

About ParabolasÉ

Are these parabolas ÒparallelÓ to teach other? What does it mean
for two curves to be parallel?
Does it mean that the tangent lines at each x value are parallel on both
curves?

They will always be 10 units apart on the vertical sense of
distance.

Æd

Adding a constant just moves the parabola up and down.

Problem, express Æd in terms of k and d.

Æd = 5 (approx.), k=10 d=25

This is the model of a Òreal-life application.Ó On some of the driving ranges (for
people who enjoy something like golf).
At a driving range, you may be up on a platform when you drive the ball.
Knowing this Æd will help determine how far you actually drove the ball.

To solve:

Express the ÒlowerÓ curve as f(x) = -ax(x-d) + k and the
ÒupperÓ curve as g(x) = -a[x-(d+Æd)] [x + Æd]. If we equate f(x) and g(x), weÕll be able to solve for Æd.

Discussion about
looking at (or for) some application of the Geometric Mean within this problem.

Another problem:

Next Problem:

120 degree Triangle.

This is NOT going to be an isosceles right triangle. Claim: the ratio of BA/AC = ABÕ(BÕC)
– may be helpful in proving this problem. (Consider incircle as well.)