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 max height of the arrow.

Answer 1

The highest point (maximum) occurs at the vertex, ( h, k ), in f(x) = a(x - h)² + k.

f(x) = -16x² + 200x + 4 must be put into that form using completion of the square.

 

f(x) = -16(x² - 12.5x         ) + 4

f(x) = -16(x² - 12.5x + (12.5/2)²) + 4  - (-16(12.5/2)² ) I added - 16(12.5/2)² to the parentheses, I have to subtract it outside to not change the value.

 

f(x) = -16(x - 6.25)² + 629

 

The vertex is at ( 6.25, 629 ). The maximum height is 629 feet at 6.25 seconds.