Question

What is the axis of symmetry and vertex for the graph `y = 3x^2 - 7x - 8`?

Answer 1

The axis of symmetry isthe line `x=7/6`
The vertex is `(7/6,-145/12)`

Explanation:

We know the shape of the graph , a parabola, in the same basic form as `y=x ^2` it will have a minimum point.
The minimum point is where the gradient of the curve is 0
Differentiate
`dy/dx=6x-7`

`6x-7=0` or the gradient is zero, when `x=7/6`

So the line `x=7/6` is the line of symmetry.

Put this x value into the original equation to find the y coordinate of the vertex