Type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar(s). rewrite the following equation in the form y = a(x - h)2 + k. then, determine the x-coordinate of the minimum. y = 2x2 - 32x + 56

The equation is  

                        .

Factoring 2, we get 
 
                        .

We notice that , so .

Substituting in the previous equation, we have:

                       , 

distributing 2 over the two terms inside the brackets, we finally get:

                                   

This is a parabola opening upwards, since the coefficient of x^2 in the original equation is positive, and whose vertex is (8, -72), which is the lowest point of this parabola.

  ; x-coordinate of the minimum: 8.

Can you provide the tape diagram?