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February 1, 2015

February 1, 2015

Posted by **Aria** on Tuesday, June 5, 2012 at 10:00pm.

a.) Create a function in vertex form that relates these distances. Cohen is at the origin of the graph. Assume that the ball stops when it hits the ground.

b.) Determine the restrictions on the domain and range of this function.

c.) How high is the ball when it is 45 yd. from Cohen?

- math -
**MathMate**, Tuesday, June 5, 2012 at 11:47pmThe standard quadratic equation in canonic form is

f(x)=y=a(x-h)+k

where (h,k) is the vertex.

when a<0, parabola is concave down.

So

for Cohen, h=120, k=24, so

f(x)=a(x-60)^2+24

However, we also know that y=0 at x=0 and x=120, so

f(x)=x(x-120)

Equate the two forms of f(x):

ax(x-120)≡a(x-60)^2+24

ax²-120ax≡ax²-120ax+3600a+24

Since if the two sides are equivalent, the coefficients of all powers are equal. This means:

3600a+24=0, or

a=-24/3600=-1/150

so

f(x)=-(a-60)^2/150+24

dom f(x)= R

range f(x) = (-∞,24]

I'll leave part (C) to you as an exercise.

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