{"@context":"https://schema.org/","@type":"Quiz","name":"

What is the minimum value of the function $f$ defined by $f(x)=(x-2)^{2}-4$?

","hasPart":{"@type":"Question","typicalAgeRange":"12-22","educationalAlignment":[{"@type":"AlignmentObject","alignmentType":"educationalSubject","targetName":"SAT"},{"@type":"AlignmentObject","alignmentType":"educationalLevel","targetName":"SAT","educationalFramework":"Common Core","targetUrl":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-211"}],"about":{"@type":"Thing","name":"Math, Advanced Math, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Advanced Math","Duplicate"],"name":"

What is the minimum value of the function $f$ defined by $f(x)=(x-2)^{2}-4$?

","comment":{"@type":"Comment","text":"

Choice A is correct. The given quadratic function $f$ is in vertex form, $f(x)=(x-h)^{2}+k$, where $(h,k)$ is the vertex of the graph of $y=f(x)$ in the $xy$-plane. Therefore, the vertex of the graph of $y=f(x)$ is $(2,-4)$. In addition, the $y$-coordinate of the vertex represents either the minimum or maximum value of a quadratic function, depending on whether the graph of the function opens upward or downward. Since the leading coefficient of $f$ (the coefficient of the term $(x-2)^{2}$) is 1, which is positive, the graph of $y=f(x)$ opens upward. It follows that at $x=2$, the minimum value of the function $f$ is $-4$.

Choice B is incorrect and may result from making a sign error and from using the $x$-coordinate of the vertex. Choice C is incorrect and may result from using the $x$-coordinate of the vertex. Choice D is incorrect and may result from making a sign error.

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What is the minimum value of the function $f$ defined by $f(x)=(x-2)^{2}-4$?

","suggestedAnswer":[{"@type":"Answer","position":1,"encodingFormat":"text/html","text":"

$-2$

"},{"@type":"Answer","position":2,"encodingFormat":"text/html","text":"

$2$

"},{"@type":"Answer","position":3,"encodingFormat":"text/html","text":"

$4$

"}],"acceptedAnswer":{"@type":"Answer","position":0,"encodingFormat":"text/html","text":"

$-4$

","comment":{"@type":"Comment","text":"

"},"answerExplanation":{"@type":"Comment","text":"

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