# Quadratic Functions and Parabolas : Maximum Height and Maximum Area

(1) Suppose a baseball is shot up from the ground straight up with an initial velocity of 32 feet per second. A function can be created by expressing distance above the ground, s, as a function of time, t. This function is s = -16t2 + v0t + s0

?16 represents ½g, the gravitational pull due to gravity (measured in feet per second 2).

?v0 is the initial velocity (how hard do you throw the object, measured in feet per second).

?s0 is the initial distance above ground (in feet). If you are standing on the ground, then s0 = 0.

(a) What is the function that describes this problem?

(b) The ball will be how high above the ground after 1 second?

(c) How long will it take to hit the ground?

(d) What is the maximum height of the ball?

(2) Amanda has 400 feet of lumber to frame a rectangular patio (the perimeter of a rectangle is 2 times length plus 2 times width). She wants to maximize the area of her patio (area of a rectangle is length times width). What should the dimensions of the patio be, and show how the maximum area of the patio is calculated from the algebraic equation. Use the vertex form to find the maximum area.

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#### Solution Summary

Maximum height and maximum area are found using quadratic functions. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.