What is the vertex form of #y=3x^2+2x+4#?

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Answer 1 · 2015-11-19T22:28:57

You can complete the square or use this trick ...

First, here is the vertex form of a parabola (quadratic):

#y=g(x-h)^2+k#

We can find h and k very quickly using this trick and recalling that the general formula for a quadratic is #y=ax^2+bx+c#:

#h = -b/(2a)=(-2)/(2xx3)=-1/3#

#k=y(h)=3(-1/3)^2+2(-1/3)+4=11/3#

Now, going back to vertex form, plug in h and k:

#y=g(x+1/3)^2+11/3#

Last, simply determine what is g by plugging in a known coordinate from the original equation like #(0,4)#:

#4=g(0+1/3)^2+11/3=(1/9)g+11/3#

Solving for g:

#g=3#

So, here is the vertex form:

#y=3(x+1/3)^2+11/3#

hope that helped