Parabolic path

Question

An object is thrown, and it follows a parabolic path. It's height, in meters, is given by the function f(x) = -x² + 3x + 6. Find the maximum height that the object may reach.

Answer 1

I'm assuming you don't know calculus, so you want to use the rule that for a parabola in the form ax^2 + bx + c

the vertex is located at x = -b / (2a).  If a is positive the vertex is the minimum value of the parabola, if a is negative the vertex is the maximum value.  

 

You have a = -1 and b = 3, so the vertex is located at x = -3 / (-2) = 3/2  

 

f(3/2) = -(3/2)^2 + 3(3/2) + 6 = -9/4 + 9/2 + 6 = -9/4 + 18/4 + 24/4 = 33/4 = 8 and (1/4) meters