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

Answer:

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

Step-by-step 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.