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Which equation is the inverse of [tex]2(x-2)^2 = 8(7 + y)[/tex]?

A. [tex]-2(x-2)^2 = -8(7 + y)[/tex]

B. [tex]y = \frac{1}{4} x^2 - x - 6[/tex]

C. [tex]y = -2 \pm \sqrt{28 + 4x}[/tex]

D. [tex]y = 2 \pm \sqrt{28 + 4x}[/tex]

Sagot :

GinnyAnswer
To find the inverse of the given equation \(2(x-2)^2 = 8(7+y)\), we need to isolate \(y\) in terms of \(x\). Here’s a step-by-step process to do this:

1. Start with the given equation:
[tex]\[ 2(x-2)^2 = 8(7+y) \][/tex]

2. Divide both sides by 8 to simplify:
[tex]\[ \frac{2(x-2)^2}{8} = 7 + y \][/tex]
[tex]\[ \frac{(x-2)^2}{4} = 7 + y \][/tex]

3. Subtract 7 from both sides to isolate \(y\):
[tex]\[ \frac{(x-2)^2}{4} - 7 = y \][/tex]

Thus, the equation for \(y\) in terms of \(x\) is:
[tex]\[ y = \frac{(x-2)2}{4} - 7 \][/tex]

From the options provided, the correct inverse equation is:
[tex]\[ \boxed{[(x - 2)^2/4 - 7]} \][/tex]
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