
Austin Y. answered 06/05/21
Experienced math tutor specialized in Algebra, Geometry and Calc
The answer is 80.36 meters
You are trying to find the y value of the vertex of the parabola in this case.
It is good to memorize that the x value of a parabola, y = ax2+bx+c, is x = -b/(2a), so x would be -820/(2*-4500) = 0.09111. Plugging x = 0.09111 back to the equation we can get y = 80.3556 meters.
If you didn't know x value of a parabola's vertex is -b/(2a), you can get it by changing y = ax2+bx+c to a vertex form of y = a(x-h)2+k where the vertex is at (h,k).
y = ax2+bx+c
y = a(x2+(b/a)x)+c
y = a(x2+(b/a)x+(b/a)2/4)+c-a(b/a)2/4
y = a(x+(b/a)/2)2 + something not important
y = a(x-h)2+k
Therefore, h = x value of parabola's vertex = -(b/a)/2 = -b/(2a)