What is the first step when rewriting y = 6x^2 + 18x + 14 in the form y = a(x – h)^2 + k?

y = 6(x -(-3/2))^2 - 13/12

Step-by-step explanation:

Given:  6x^2+18x+14

We have to write in vertex form y = a(x -h)^2 + k

Step 1: In the given function y = 6x^2 + 18x + 14, the coefficient of x^2 is 6, we need to make it 1, so we take out 6 and factor it.

y = 6(x^2 + 3x + 7/6)

x^2 + 3x + 7/6, the value of b = 3, now divided 3 by 2, then square it.

(3/2)^2 = 9/4

Now add and subtract 9/4

y = 6(x^2 + 3x +9/4 -9/4 + 7/6)

y = 6(x +3/2)^2 -9/4+ 7/6

y = 6(x -(-3/2))^2 +  (-27+14/24)

Here we simplified -9/4 + 7/6 taking the LCD as 12

y=6(x-(-3/2))^2(-13/12)

This can be written as

y = 6(x -(-3/2))^2 - 13/12