Algebra homework

Question

An archer's arrow follows a parabolic path. The height of the arrow f(x) is given by f(x) = -16x² + 200x + 4, in feet. Find the maximum height of the arrow

Answer 1

Hi Claudia,

 

-16x² + 200x + 4  Lets do "completing the square" method 

 

-16 (x² - 12.5x - 0.25)

 

-16 (x² - 12.5x + 39.065       - 39.065 - 0.25) 

 

-16(x-6.25)² -39.315

 

With -39.3125 being constant, the above expression is the maximum when (x-6.25) is at the minimum.

set it to zero and x_{min = 6.25}

At that point the y value becomes -39.315

I hope this helps

Answer 2

There are two ways of doing it; obtaining the derivative (calculus) or simply using the formula x = -b/2a. 

Since you're in Algebra, the latter would be the most ideal: x = -b/2a. The "x" in this formula is giving you the x-coordinate when the y-coordinate is either highest or lowest. Since the "a" in this quadratic equation is negative, then it is a maximum because the graph will warp downward.

 

Note: standard form for quadratic equation is: f(x) = ax² + bx + c

in this case: a = -16, b = 200, c = 4

 

x = - (200)/[(2)(-16)] = 6.25

y(6.25) = -16(6.25²) + 200(6.25) + 4 = 629 <----- answer