Question

The y coordinate of the vertex of f (x)=-x^2+8x+7 is f(4)

Answer 1

Hello there.

To answer this question, we need to remember some properties about the vertex of quadratic functions.

Let
`f(x)=ax^2+bx+c,~a\\eq0`. Its vertex can be found on the coordinates
`(x_v,~y_v)` such that
`x_v=-(b)/(2a)` and
`y_v=-(b^2)/(4a)+c`, in which
`y_v=f(x_v)`.

Using the coefficients given by the question, we get that:

`x_v=-(8)/(2\cdot(-1))\\\\\\ x_v=-(8)/(-2)\\\\\\ x_v=4`

Thus, we have:

`y=f(x_v)=f(4)`

So the statement is true, because the
`x` coordinate of the vertex of the function is equal to
`4.~~\checkmark`