Question

What are the coordinates of the vertex of the graph of the function y = -x^2 + 6x + 11?

Answer 1

To find the coordinates of the vertex of the graph of the function y = -x^2 + 6x + 11, we use the formula for the x-coordinate of the vertex of a quadratic function, which is given by:

x = -b/(2a)

In this case, a = -1 and b = 6, so we have:

x = -6/(2*(-1))
x = -6/-2
x = 3

Next, we substitute x = 3 back into the original function to find the y-coordinate:

y = -3^2 + 6(3) + 11
y = -9 + 18 + 11
y = 20

Therefore, the vertex of the graph of the function y = -x^2 + 6x + 11 is located at the point (3, 20).