Question

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

Answer 1

Answer:

The vertex of the parabola is (3, 4)

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:

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

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)