Question

I need help asap label vertex

Answer 1

ANSWER

$(0.5,-4.75)$

EXPLANATION

We want to find the coordinates of the vertex of the equation:

$f(x)=-x^2+x-5$

The general form of a parabolic equation is:

$f(x)=ax^2+bx+c_{}$

The x-coordinate of the vertex of a parabola can be found by using the formula:

$h=-\frac{b}{2a}$

From the given equation:

$\begin{gathered} a=-1 \\ b=1 \end{gathered}$

This implies that the x-coordinate of the vertex of the parabola is:

$\begin{gathered} h=-\frac{1}{2(-1)}=-\frac{1}{-2} \\ h=\frac{1}{2}=0.5 \end{gathered}$

To find the y-coordinate, substitute the value of h for x in the equation.

That is:

$\begin{gathered} f(h)=f(\frac{1}{2})=-(\frac{1}{2})^2+(\frac{1}{2})-5 \\ f(\frac{1}{2})=-\frac{1}{4}+\frac{1}{2}-5 \\ f(\frac{1}{2})=-4.75 \end{gathered}$

Therefore, the vertex of the parabola is:

$(0.5,-4.75)$