First change the quadratic into the f(x)=a(x-h)^2 +k form. 2x^2 -12x+16 then find the vertex. explain your steps.

Refresh the page or reopen the answer if you see errors.  as a side note, perfect square triomials: ======    to convert this into  we need to complete the square.since the leading coefficient (the coefficient on x²) is not 1, factor out the leading coefficient of 2 from the first 2 terms.      inside, with  , we add a constant to be able to factor it as a perfect square trinomial.  this constant comes halving the coefficient on x and then squaring the result.the coefficient of x in  is  .dividing that in half gets us  squaring that gets us  .so we need a constant term of 9 in to be able to factor it as a perfect square.but we need to add and subtract 9 in order to retain algebraic balance. we cannot just simply add 9, otherwise we will change the original expression. but if we add 0, nothing changes. so by adding and subtracting 9, it is still the same expression.      we need to take  out of the parentheses to factor it properly. as we take it out, we need to multiply by the coefficient over the parentheses as it comes out.      the trinomial  factors into  .      alternate way, without doing that "take out -9" stepfactor  inside of the parentheses      then distribute the 2      ======a parabola with the form  has its vertex at  .so looking at  , we see that h = 3 and k = -2.so the vertex is at