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  

                        [tex]y=2x^2-32x+56[/tex].

Factoring 2, we get 
 
                        [tex]y=2(x^2-16x+28)[/tex].


We notice that [tex](x-8)^2=x^2-16x+64[/tex], so [tex]x^2-16x=(x-8)^2-64[/tex].

Substituting in the previous equation, we have:

                       [tex]y=2(x^2-16x+28)=2[(x-8)^2-64+28]=2[(x-8)^2-36][/tex], 

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

                                   [tex]y=2(x-8)^2-72.[/tex]


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.


Answer:  [tex]y=2(x-8)^2-72.[/tex]; x-coordinate of the minimum: 8.