Question

How do you find the axis of symmetry and vertex point of the function: `f(x)= 3x^2+12x-6`?

Answer 1

The vertex is `(1,9)`
The axis of symmetry is `x=1`

Explanation:

To find the axis of symmetry of the function, use the coefficients of the equation and the formula `x = -b/2a`

For the function `f(x) = 3x^2 + 12x - 6`
`a = 3`
`b = 12`
`c = -6`

The x of the vertex and the axis of symmetry can be found by
`-b/2a`
`-12/(2(-6))`
`x = 1`

This means the x of the vertex is x = 1 which is also the line of symmetry for the function.

To find the y of the vertex, plug x = 1 into the function and solve for y

`y = 3(1)^2 + 12(1) -6`
`y = 3 + 12 -6`
`y = 9`

Therefore the vertex point is `(1 , 9)`