Question

How do you graph and label the vertex and axis of symmetry `y=-6x^2-4x+1`?

Answer 1

We need to find the vertex of the parabola, and then we'll also get the axis of symmetry (it will have the same x-coordinate as the vertex). To find the vertex of the parabola, we'll use the formula to find the x-coordinate of the vertex. If you have an equation of a parabola of the form `y=ax^2+bx+c`, the x-coordinate of the vertex is given by:
`-b/(2a)`

In our case, we get:
`-(-4)/-12=-1/3`

This is the x-coordinate, and to get the y-coordinate we plug it into our function:
`-6(-1/3)^2-4(-1/3)+1=-6*1/9+4/3+1=`

`=-6/9+4/3+3/3=-2/3+7/3=5/3`

This means that the vertex is at `(-1/3,5/3)`, and the axis of symmetry will be at the same x-coordinate, `x=-1/3`