Question 253584
They are asking you at what value x will give the largest value of y. Quadratics always produce a graph called a parabola. In this case the parabola is inverted (upside down) because the coefficient of x^2 is a minus number.

In essence, we need to find when the parabola peaks or when the gradient is zero.

We can do this by differentiation. dy/dx = -0.2x+9.This gives the gradient at any given value of x. We want the gradient to be zero so 0= -0.2x+9 so x = 45.

If we plot the graph of y= -0.1x^2+9x-50 we can see that this is true.

{{{ graph( 500, 400,-5, 50, -10, 200, -0.1x^2+9x-50) }}}