Question

I need help asap label vertex

Answer 1

`(0.5,-4.75)`

Step-by-step 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=-(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=-(1)/(2(-1))=-(1)/(-2) \\ h=(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((1)/(2))=-((1)/(2))^2+((1)/(2))-5 \\ f((1)/(2))=-(1)/(4)+(1)/(2)-5 \\ f((1)/(2))=-4.75 \end{gathered}`

Therefore, the vertex of the parabola is:

`(0.5,-4.75)`