# The equation and graph of a polynomial are shown below the graph reaches it's maximum when the value of x is 3 what is the y value of this maximum y=-x^2+6x-7?

You need to evaluate the polynomial at the maximum $x = 3$,
For any value of $x , y = - {x}^{2} + 6 x - 7$, so replacing $x = 3$ we get:
$y = - \left({3}^{2}\right) + 6 \cdot 3 - 7 = - 9 + 18 - 7 = 18 - 16 = 2$, so the value of $y$ at the maximum $x = 3$ is $y = 2$
Please note that this doesn't prove that $x = 3$ is the maximum