Question

The axis of symmetry for the function f(x) = -x^2 - 10x + 16 is x = -5. What are the coordinates of the vertex of the graph?

Answer 1

The x coordinate is -5.

The y coordinate is equal to
`f(-5)`


`f(-5)=-(-5)^2-10\cdot(-5)+16=-25+50+16=41`

So the vertex is
`(-5,41)`

Answer 2

(x, f(x))= (-5, 41)

Explanation:

Your function is a parable, then you have the axis of symmetry which is the straight line that divides your graph in half, this is X = -5,

If you replace this value of X in the original equation
`f(-5)=-(- 5)^2-(10*(-5))+16`

you get
`f(-5)=-(25)+50+16` the result is 41, which is the value on the other axis.

Therefore the coordinates of the parabola vertex are (x, f(x))=(-5,41)

This means the coordinates (vertex) where the function reaches a maximum or minimum value, in this case the maximum.