Word Problem

Question

An archer's arrow follows a parabolic path. The height of the arrow f(x) is given by f(x)=-16x squared + 200x + 4, in feet. Find the maximum height of the arrow.

Answer 1

One method for finding a maximum or minimum is putting the quadratic in vertex form.  To do so, one must complete the square.  This process has the following steps:

 

1) factor a constant out of your x-terms

2) divide the 2nd term in the parenthesis by 2, square it and add it in the parentheses

3) multiply that value by your constant and subtract it at the end

 

The result should be in the form of y=a(x-h)^2+k

With the max/min at (h, k)

 

y = -16x^2 + 200x +4

y = -16(x^2 - 12.5x) + 4

y = -16(x^2 - 12.5x + 39.0625) + 4 -(39.0625•-16)

y = -16(x - 6.25)^2+629

 

The vertex if this parabola is (6.25, 629) so the maximum height of the arrow is 629 ft