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

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