Question

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Answer 1

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

Answer 2

Step-by-step explanation:

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

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

Adding and subtracting 64 :

$y=2(x^2-16x+64-64+28)[tex]y=2(x^2-16x+64) +2(-64+28)$

$y=2(x^2-2\times x\times 8+8^2) +2(-36)$

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

$y=2\times (x-8)^2-72$

$y=2\times (x-8)^2+(-72)$

Putting, x = 8

$y=2\times (8-8)^2+(-72)$

y = -72