Question

Write y=2x^2+12x+14 In vertex form

Answer 1

Answer:

$\large\boxed{y=2(x+3)^2-6}$

Step-by-step explanation:

The vertex form of a parabola f(x) = ax² + bx + c:

$y=a(x-h)^2+k$

(h, k) - vertex

$h=\dfrac{-b}{2a}\\\\k=f(h)$

We have the equation:

$y=2x^2+12x+14\\\\a=2,\ b=12,\ c=14\\\\h=\dfrac{-12}{2(2)}=\dfrac{-12}{4}=-3\\\\k=f(-3)=2(-3)^2+12(-3)+12=2(9)-36+12=18-36+12=-6$

Finally:

$y=2(x-(-3))^2+(-6)=2(x+3)^2-6$