Question

What is the vertex of the parabola represented by y = - x^2 + 6x - 5-x has a variable of 2

Answer 1

The vertex of the parabola is (3, 4)

Step-by-step explanation:

Given the equation:

`y=-x^2+6x-5`

This is in the form:

`y=ax^2+bx+c`

With a = -1, b = 6, and c = -5

The x-coordinate of the vertex is given as:

`\begin{gathered} x=-(b)/(2a) \\ \\ =-(6)/(2(-1)) \\ \\ =(6)/(2) \\ \\ =3 \end{gathered}`

Substituting x by 3 in the equation of the parabola, we can obtain the y-coordinate of the vertex.

Doing that, we have:

`\begin{gathered} y=-(3^2)+6(3)-5 \\ =-9+18-5 \\ =4 \end{gathered}`

Therefore, the vertex of the parabola is (3, 4)