Derivatives : Maximizing Functions and Finding a Vertex
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1. Express the function in the form f(x) = a(x-h)2 + K and indicate the vertex.
a. f(x) = -x^2 + 13x - 8
b. f(x) = 4x^2 - 8x + 1
2. An object is thrown upward from the top of a 160-foot (Ho) building with an initial velocity (Vo) of 48 feet per second. How long after the object is projected upward will it strike the ground?
3. The profit that a vendor makes per day by selling X pretzels is given by the function P(x) = -0.004x^2 + 2.8x - 350. Find the number of pretzels that must be sold to maximize profit.
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Solution Summary
Functions are maximized and a vertex is found and discussed in the solution.
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Express the function in the form f(x) = a(x-h)2 + K and indicate the vertex.
f(x) = -x2 + 13x - 8
= -(x2 - 13x + 8)
= -(x2 - 13/2 * 2x + (13/2)2 - (13/2)2 + 8)
= -(x2 - 13/2 * 2x + (13/2)2) + 169/4 - 8
= -(x - 13/2)2 + (169-32)/4
= -(x - 13/2)2 + 137/4
= a(x - h)2 + ...
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