Math 1322 Pre-calculus Notes on Section 2.3 Dr. Cordero

__Problem # 39__

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a. Complete the square to obtain the equation of a parabola in standard form:

The maximum distance is the maximum value of this function, that is, 424 ft.

b. The distance above the ground is s(0). The answer is 100 ft.

__Problem
# 40__

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a. Since after 12 seconds the object is at the ground , set and solve for .

. The answer is 192 ft/sec.

b. To find the maximum distance, complete the square to obtain the equation of a parabola in standard form: . The answer is 576 ft.

__Problem
# 44:__

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Since the path is parabolic starting at (0,0) and ending at (9, 0) the midpoint is 9/2.

Since the maximum height off the ground is 3 ft, the vertex of the parabola is (9/2, 3).

Thus the equation is

Now use the given information to compute . The value of a is -4/27.

__Problem
# 51__

Notice that
since the price of each pair is reduced after the 50^{th} pair, the
maximum is not obtained when the maximum number of pairs of shoes is sold; that
is, the maximum is not attained when 600 pairs are sold. To find the point where
the maximum is attained start with the equation
. Complete the square to obtain the equation of a parabola in
standard form and from this equation obtain the value of x that gives the
maximum value of the function.