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

$$f(x)=x^{2}-18x-360$$

If the given function $f$ is graphed in the $xy$-plane, where $y=f(x)$, what is an $x$-intercept of the graph?

","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-131"}],"about":{"@type":"Thing","name":"Math, Advanced Math, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Advanced Math","Duplicate"],"name":"

$$f(x)=x^{2}-18x-360$$

If the given function $f$ is graphed in the $xy$-plane, where $y=f(x)$, what is an $x$-intercept of the graph?

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

Choice A is correct. It's given that $y=\\bm{f}(\\bm{x})$. The $x$-intercepts of a graph in the $xy$-plane are the points where $y=0$. Thus, for an $x$-intercept of the graph of function $f,0=\\bm{f}(\\bm{x})$. Substituting $0$ for $f(\\bm{x})$ in the equation $\\bm{f}(\\bm{x})=\\bm{x}^{2}-18\\bm{x}-360$ yields $0=\\bm{x}^{2}-18\\bm{x}-360$. Factoring the right-hand side of this equation yields $0=(\\bm{x}+12)(\\bm{x}-30)$. By the zero product property, $\\bm{x}+12=0$ and $\\bm{x}-30=0$. Subtracting $12$ from both sides of the equation $\\bm{x}+12=0$ yields $\\bm{x}=-12$. Adding $30$ to both sides of the equation $\\bm{x}-30=0$ yields $\\bm{x}=30$. Therefore, the $x$-intercepts of the graph of $\\bm{y}=\\bm{f}(\\bm{x})$ are $(-12,0)$ and $(30,0)$. Of these two $x$-intercepts, only $(-12,0)$ is given as a choice.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

"},"encodingFormat":"text/markdown","text":"

$$f(x)=x^{2}-18x-360$$

If the given function $f$ is graphed in the $xy$-plane, where $y=f(x)$, what is an $x$-intercept of the graph?

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

$(-30,0)$

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

\$(-360,0)\$

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

$(12,0)$

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

$(-12,0)$

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

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

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-131"}

$$f(x)=x^{2}-18x-360$$If the given function $f$ is graphed in the $xy$-plane, where $y=f(x)$, what is an $x$-intercept of the graph?

$$f(x)=x^{2}-18x-360$$If the given function $f$ is graphed in the $xy$-plane, where $y=f(x)$, what is an $x$-intercept of the graph?

$$f(x)=x^{2}-18x-360$$If the given function $f$ is graphed in the $xy$-plane, where $y=f(x)$, what is an $x$-intercept of the graph?

$$f(x)=x^{2}-18x-360$$

If the given function $f$ is graphed in the $xy$-plane, where $y=f(x)$, what is an $x$-intercept of the graph?

$$f(x)=x^{2}-18x-360$$

If the given function $f$ is graphed in the $xy$-plane, where $y=f(x)$, what is an $x$-intercept of the graph?

$$f(x)=x^{2}-18x-360$$

If the given function $f$ is graphed in the $xy$-plane, where $y=f(x)$, what is an $x$-intercept of the graph?