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

1 Answer
Aug 24, 2016

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