Question

What is the axis of symmetry and vertex for the graph `y=-x^2+2x-5`?

Answer 1

`x= 1` is the line of symmetry and the vertex is at `(1,-4)`

Explanation:

This is the equation of a parabola with the standard form

`y = ax^2 + bx + c`

To find the axis of symmetry (a vertical line), use the formula:
`x = (-b)/(2a)`.

This will give you the x-value which is exactly in the middle of the parabola.

`x = (-2)/(2xx-1) = (-2)/(-2) = 1`

The vertex (or turning point) lies on the axis symmetry.

So, if `x = 1,` then find the `y` value by substituting into the original equation

`y = -(1)^2 + 2(1) - 5`

`y = -1 +2 -5 = -4`

So the vertex is at (1 -4)