How do you graph and identify the vertex and axis of symmetry for y=1/3x^2-2x-3?

1 Answer
Dec 13, 2017

The Axis of symmetry is the vertical line x=3

The coordinates of the vertex are (3,-6)

Explanation:

This is a quadratic function in the form ax^2+bx+c=y. With a=(1/3), b=-2, and c=-3
When in this form the axis of symmetry is the vertical line x=-b/(2a)
Here this becomes x=-(-2)/(2(1/3))=3.
This is the line of symmetry and the x value of the vertex.

The y value of the vertex is then found by plugging the x value of the line of symmetry into the original equation and solving for y
y=(1/3)x^2-2x-3=(1/3)(3)^2-2(3)-3=-6

So the coordinates of the vertex are (3,-6)