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

Problem # 39

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

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:

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 50th 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.