Question

A grasshopper jumps from the ground. The path of the grasshopper is modeled by the equation y=−0.5x2+8x where x is the horizontal distance the grasshopper travels and y is its height.

Answer 1

Please use " ^ " to indicate exponentiation:  y=−0.5x^2+8x 

Examining this function, we see that its graph is a vertical parabola opening down.

You did not supply instructions for this problem.
However, one could guess that you might want to find the highest point of the grasshopper's path.  To do this, find the vertex:  Find the x value defined by 

x = -b/(2a).  Here, a= -0.5 and b= 8.  Thus, the vertex is at x = -8/(2[-0.5]), or 

x -8/(-1) = 8 units.  The corresponding y value is then 

y =  −0.5*8^2+8(8)  = -0.5(64) + 64, or 32 units.