Question

convert 3x2-10x+2 to vertex form

Answer 1

have you attempted this?

Answer 2

Usually the procedure to go from standard form to vertex form is by completing the square:
If you have a standard form \(ax^2+bx+c\) where \(a\ne 1\) (and \(\ne 0\) too), then you can factor out \(a\) and then attempt to complete the square on the remaining quadratic: \[\large 3x^2 -10x+2=3\left( x^2-\frac{10}{3}x+\frac{2}{3}\right)\] Then what you can do is add and subtract the term \( \large \left(\frac{b}{2a}\right)^2=\left( \frac{-10}{3(2)}\right)^2=\frac{25}{9}\) : \[ \large 3\left(x^2 -\frac{10}{3}x\color{red}{+\frac{25}{9}-\frac{25}{9}}+\frac{2}{3}\right) \]
The rest consists of writing the first 3 terms in the parentheses as a perfect square polynomial (something of the form \((x-a)^2\) ) and just add the last 2 terms together