Question

Could someone explain to me on how to turn 3x^2+12x+5 to vertex form?

Answer 1

yes
you know it is going to look like
\[y=3(x-h)^2+k\] so you need to find \(h\) and \(k\)
\(h\) is the first coordinate of the vertex, which is always \(-\frac{b}{2a}\) which in your case is \[-\frac{12}{2\times -3}=2\]

Answer 2

now we have
\[3(x-2)^2+k\] and \(k\) is the second coordinate of the vertex, which you can find by replacing \(x\) by \(2\) in the original equation, and see what you get

Answer 3

Thank you so much for your help.