which equation is the inverse of $2(x - 2)^2 = 8(7 + y)$?

$-2(x - 2)^2 = -8(7 + y)$

$y = \frac{1}{4}x^2 - x - 6$

$y = -2 \pm \sqrt{28 + 4x}$

$y = 2 \pm \sqrt{28 + 4x}$

Question

which equation is the inverse of $2(x - 2)^2 = 8(7 + y)$?

$-2(x - 2)^2 = -8(7 + y)$

$y = \frac{1}{4}x^2 - x - 6$

$y = -2 \pm \sqrt{28 + 4x}$

$y = 2 \pm \sqrt{28 + 4x}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Finding Inverses Algebraically" ], "new_concepts": [], "current_concepts": [ "Inverse Functions", "Finding Inverses Algebraically" ] } ## Swap variables x and y $$ 2(y-2)^2 = 8(7+x) $$ ## Isolate the squared term $$ (y-2)^2 = 4(7+x) = 28 + 4x $$ ## Solve for y $$ \begin{aligned} y-2 &= \pm\sqrt{28+4x} \ y &= 2 \pm \sqrt{28+4x} \end{aligned} $$

(A) $-2(x-2)^2 = -8(7+y)$

(B) $y = \frac{1}{4}x^2 - x - 6$

(C) $y = -2 \pm \sqrt{28+4x}$

(D) $y = 2 \pm \sqrt{28+4x}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Finding Inverses Algebraically" ] }

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QUESTION IMAGE

Question

Explanation:

Swap variables x and y

Isolate the squared term

Solve for y

Answer: