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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.

Type the correct answer in each box Use numerals instead of words If necessary use for the fraction bars Rewrite the following equation in the form y ax h2 k Th class=

Respuesta :

Edufirst
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

Step-by-step explanation:

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

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

Adding and subtracting 64 :

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

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

[tex]y=2(x^2-2\times x\times 8+8^2) +2(-36)[/tex]

Using identity : [tex](a+b)^2=a^2-2ab+b^2[/tex]

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

[tex]y=2\times (x-8)^2+(-72)[/tex]

Putting, x = 8

[tex]y=2\times (8-8)^2+(-72)[/tex]

y = -72

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