Question

How do you find the axis of symmetry and vertex point of the function: `y=3x^2 -8x +7`?

Answer 1

Axis of Symmetry: `x=4/3`
Vertex: `(4/3,5/3)`

Explanation:

First, you will have to convert the equation into vertex form `y=a(x-h)^2+k` by "completing the square". Afterwards, it will be easy to determine the axis of symmetry and the vertex:

Axis of Symmetry: `x=h`
Vertex: `(h,k)`

Solution
`y=3x^2−8x+7`
`y-7=3x^2−8x`
`y-7=3(x^2−8/3x)`
`y-7+3(16/9)=3(x^2−8/3x+16/9)`
`y-7+16/3=3(x−4/3)^2`
`y-21/3+16/3=3(x−4/3)^2`
`y-5/3=3(x−4/3)^2`
`color(blue)(y=3(x−4/3)^2+5/3)`

Axis of Symmetry
In the equation, `h=4/3`. Therefore the axis of symmetry is:
`x=h`
`color(red)(x=4/3)`

Vertex
In the equation, `h=4/3` and `k=5/3`. Therefore, the vertex is:
`(h,k)`
`color(red)((4/3,5/3)`