Question

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.

Answer 1

Explanation:

`y = 2x^2-32x+56`

`y=2(x^2-16x+28)`

Adding and subtracting 64 :

`y=2(x^2-16x+64-64+28)</p><p>[tex]y=2(x^2-16x+64) +2(-64+28)`

`y=2(x^2-2* x* 8+8^2) +2(-36)`

Using identity :
`(a+b)^2=a^2-2ab+b^2`

`y=2* (x-8)^2-72`

`y=2* (x-8)^2+(-72)`

Putting, x = 8

`y=2* (8-8)^2+(-72)`

y = -72

Answer 2

Given: y = 2x^2 - 32x + 56

1) y = 2 [ x^2 - 16x] + 56

2) y = 2 [ (x - 8)^2 - 64 ] + 56

3) y = 2 (x - 8)^2 - 128 + 56

4) y = 2 (x - 8)^2 - 72 <----------- answer

Minimum = vertex = (h,k) = (8, - 72)

=> x-ccordinate of the minimum = 8 <-------- answer