Mathematics: What is the first step when rewriting y = 6x2 + 18x + 14 in the form y = a(x – h)2 + k? 16 must be factored from 18x + 14 x must be factored from 6x2 + 18x 6 must be factored from 6x2 + 14 6 must be factored from 6x2 + 18x

What is the first step when rewriting y = 6x2 +

justinpatengale2002

20.07.2020

Option D, 6 must be factored from 6x^2+18x

Step-by-step explanation:

Given : y=6x^2+18x+14

To find : The given equation in the form y = a(x-h)^2+k

Solution :

Now, we re-write the given equation

y=6x^2+18x+14

To covert it into vertex form y = a(x-h)^2+k where (h,k) represents the vertex.

First step is to take 6 common from 6x^2+18x

i.e, y=6(x^2+3x)+14

Now, further step is by completing the square,

$y=6(x^2+3x+\frac{3}{2}^2-\frac{3}{2}^2)+14$

$y=6(x+\frac{3}{2})^2-6\times(\frac{3}{2}^2)+14$

$y=6(x+\frac{3}{2})^2-\frac{27}{2}+14$

$y=6(x+\frac{3}{2})^2+\frac{1}{2}$

The required form is $y=6(x+\frac{3}{2})^2+\frac{1}{2}$

Where, a=6, $(h,k)=(-\frac{3}{2},\frac{1}{2})$

Therefore, Option D is correct, 6 must be factored from 6x^2+18x

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