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Which of the following graphs represents the equation 𝑦 equals 𝑥 squared minus five 𝑥 plus eight?
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We can make a table to come up with a few points to plug on these graphs.
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What is 𝑦 when 𝑥 equals zero?
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𝑦 would equal zero squared minus five times zero plus eight.
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When 𝑥 is zero, 𝑦 equals eight.
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If we plug that point on all of the graphs, we see that the lines on graphs d and e do not go through the point zero, eight.
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Graphs d and e can’t represent this equation.
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Let’s choose another value for 𝑥 to find a second point on our graph.
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Let’s consider when 𝑥 equals one.
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When 𝑥 equals one, 𝑦 equals one squared minus five times one plus eight.
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One minus five equals negative four.
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Negative four plus eight equals four.
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This graph should have a point at one, four.
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Okay, let’s consider the point one, four.
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a goes through one, four.
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b does not go one- through one, four.
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And c does not go through one, four.
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b and c cannot graph this equation.
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Using a table, we’ve narrowed down the graph to a.