Question

What is the axis of symmetry of `y=-x^2+8x-7`?

Answer 1

`x =4` is the line of symmetry.

Explanation:

The quickest and easiest method is to use the formula which does exactly this.

Note that the given graph is for a parabola (it has an `x^2` term).

The general form of and equation of a parabola is:
`y = ax^2 +bx +c`

The axis of symmetry is therefore a vertical line passing though the turning point.

All vertical lines have an equation `" "x= " a number"`

`x = (-b)/(2a)` gives the line of symmetry.

So for the parabola `y=-x^2+8x-7`

`x = (-8)/(2(-1)) " = "4` is the line of symmetry.

Another method is to find the x-intercepts by solving the equation

`-x^2+8x-7 =0` and then find the average of the two x-values.

This will give the value for the line of symmetry.