Question

The axis of symmetry for the function f(x) = −x2 − 10x + 16 is x = −5. What are the coordinates of the vertex of the graph?

Answer 1

The coordinates of the vertex are (-5, 41)

Explanation:

For a quadratic function of the form

`f(x) = ax ^ 2 + bx + c`

Where a, b and c are constants and represent the coefficients of the function, then the symmetry of the parabola always passes through its vertex.

In this case we have the following parabola

`f (x) = -x2 - 10x + 16`

And we know that its axis of symmetry is the line
`x = -5`

Then we know that this axis of symmetry passes through the vertex of the parabola.

Therefore, the x coordinate of the vertex is -5.

To find the coordinate in y of the vertex, we substitute x = -5 in the function.

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

Finally, the vertices are in the point (-5, 41).