use the inverse of the function (y = x^2 - 18x) to find the unknown values.

y = pmsqrt{bx + c} + d

(b = )
(c = )
(d = )

Question

use the inverse of the function (y = x^2 - 18x) to find the unknown values.

y = pmsqrt{bx + c} + d

(b = )
(c = )
(d = )

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Inverse Functions", "Quadratic Inverse" ], "new_concepts": [], "current_concepts": [ "Inverse Functions", "Quadratic Inverse", "Completing the Square" ] } ## Swap variables to set up the inverse equation $$ x = y^2 - 18y $$ ## Complete the square for the quadratic expression $$ \begin{aligned} x + 81 &= y^2 - 18y + 81 \ x + 81 &= (y - 9)^2 \end{aligned} $$ ## Solve for y to find the inverse function $$ \begin{aligned} y - 9 &= \pm\sqrt{x + 81} \ y &= \pm\sqrt{x + 81} + 9 \end{aligned} $$ Comparing this to $y = \pm\sqrt{bx + c} + d$: $$ b = 1,\quad c = 81,\quad d = 9 $$ Use the inverse of the function $y = x^2 - 18x$ to find the unknown values. $y = \pm\sqrt{bx + c} + d$ $b =$ 1 $c =$ 81 $d =$ 9 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Inverse" ] }

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QUESTION IMAGE

Question

Explanation:

Swap variables to set up the inverse equation

Complete the square for the quadratic expression

Solve for y to find the inverse function

Answer: