How do you find the vertex of # y = 4x^2 – 6x – 3#?

Question

3711 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-07T08:46:08

The vertex is the point at which the gradient is equal to #0#.

The vertex is the point #(3/4,-21/4)#

The vertex is the point at which the first derivative (the gradient) is equal to #0#.

#y=4x^2-6x-3#
#y'=8x-6#

#8x-6=0 -> x=6/8=3/4#

Substitute this x-value back into the original equation to find the y coordinate of the vertex:

#y=4x^2-6x-3=4(3/4)^2-6(3/4)-3#

#y= 36/16-18/4-3=9/4-18/4-12/4=-21/4#

So the vertex is the point #(3/4,-21/4)#