Answer:
The first step when rewriting [tex]y = 6\cdot x^{2}+18\cdot x + 14[/tex] consists in applying distributive property. (Step 2).
Step-by-step explanation:
We present the procedure, in which [tex]y = 6\cdot x^{2}+18\cdot x + 14[/tex] is transformed into the form [tex]y = a\cdot (x-h)^{2} + k[/tex]:
1) [tex]y = 6\cdot x^{2}+18\cdot x + 14[/tex] Given
2) [tex]y = 6\cdot \left( x^{2}+3\cdot x + \frac{7}{3}\right)[/tex] Distributive property/[tex]\frac{a\cdot c}{b\cdot c} = \frac{a}{b}[/tex]
3) [tex]y = 6\cdot \left[x^{2}+3\cdot x + \frac{7}{3}+\left(-\frac{1}{12} \right)+\frac{1}{12} \right][/tex] Modulative property/Existence of the additive inverse.
4) [tex]y = 6\cdot \left(x^{2}+3\cdot x+\frac{9}{4} \right)+6\cdot \left(\frac{1}{12}\right)[/tex] Definition of subtraction/Associative and distributive properties.
5) [tex]y = 6\cdot \left(x+\frac{3}{2} \right)^{2}+\frac{1}{2}[/tex] Perfect square trinomial/[tex]a \cdot \frac{b}{c} = \frac{a\cdot b}{c}[/tex]/Result.
As we can see, the first step when rewriting [tex]y = 6\cdot x^{2}+18\cdot x + 14[/tex] consists in applying distributive property. (Step 2).
