To rewrite the quadratic equation [tex]\( y = 6x^2 + 18x + 14 \)[/tex] in the form [tex]\( y = a(x - h)^2 + k \)[/tex], we need to start by completing the square. This involves several steps, with the first crucial step being to factor out the common factor from the [tex]\( x \)[/tex]-terms.
Let's go through the process step-by-step:
1. Identify the quadratic and linear terms: [tex]\( 6x^2 \)[/tex] and [tex]\( 18x \)[/tex].
2. Factor out the greatest common factor from these terms. The greatest common factor of [tex]\( 6x^2 \)[/tex] and [tex]\( 18x \)[/tex] is 6, so:
[tex]\[
y = 6(x^2 + 3x) + 14
\][/tex]
So, the correct first step is:
[tex]\[ \boxed{6 \text{ must be factored from } 6x^2 + 18x} \][/tex]
