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Which of the following is the equation of the function drawn on the graph?
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Here, we can see that we have a U-shaped graph.
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A quadratic function is a function where the greatest power of a variable is two, and its graph is U-shaped.
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Opening upward, if its leading coefficient is positive and opening downward, if its leading coefficient is negative.
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Therefore, we need to have a quadratic equation.
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This means we can automatically eliminate option A.
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Because its greatest power of a variable is one, this means itβs a linear function; we need a quadratic function.
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Next, we can see that our graph is opening upward.
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That means we need to have a positive leading coefficient.
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A leading coefficient is the number in front of the first term β the leading term.
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So all of our options have either a positive one in front of our π₯ squared or a negative one in front of our π₯ squared.
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Options B and C have a positive one in front of π₯ squared and options D and E have a negative one in front of π₯ squared.
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Therefore, we can eliminate options D and E because they have a negative one as their leading coefficient.
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We need a positive leading coefficient.
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This means we need to decide between option B: π of π₯ equals π₯ squared plus eight or option C: π of π₯ equals π₯ squared minus eight.
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Looking at our two options, it would be best to go ahead and take a look at the points on our graph.
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Here are a few easy points to work with for our graph.
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Letβs go ahead and pick one.
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Here, we have zero, negative eight.
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This means if we would plug in zero for π₯, we should get negative eight for a π¦.
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π of π₯ in π¦ actually means the same thing, so keep that in mind for when we plug in π₯.
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So letβs go ahead and plug in zero for π₯ for both equations and see which one would give us an answer of negative eight.
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Here we can see we have zero squared plus eight and zero squared is zero and zero plus eight is equal to eight.
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Over here, we have zero squared minus eight and zero squared is zero and zero minus eight is negative eight, which is what we wanted.
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So option C, π of π₯ equals π₯ squared minus eight, would be the correct equation for the function drawn on a graph.
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Now itβs always good to double check your work.
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So letβs go ahead and just try another point from our graph and make sure that it works.
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Letβs plug in the point three, one.
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So letβs plug in three for π₯ and make sure we get one for π¦.
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Here we can see when we plug in three, three squared is nine and nine minus eight is indeed one.
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Therefore, C, π of π₯ equals π₯ squared minus eight, is the equation of the function drawn on the graph.