Video: Identifying Graphs of Quadratic Equations in Standard Form

Which of the following graphs represents the equation 𝑦 = 𝑥² − 5𝑥 + 8? [A] Graph a [B] Graph b [C] Graph c [D] Graph d [E] Graph e.

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Video Transcript

Which of the following graphs represents the equation 𝑦 equals 𝑥 squared minus five 𝑥 plus eight?

We can make a table to come up with a few points to plug on these graphs. What is 𝑦 when 𝑥 equals zero? 𝑦 would equal zero squared minus five times zero plus eight. When 𝑥 is zero, 𝑦 equals eight. 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. Graphs d and e can’t represent this equation.

Let’s choose another value for 𝑥 to find a second point on our graph. Let’s consider when 𝑥 equals one. When 𝑥 equals one, 𝑦 equals one squared minus five times one plus eight. One minus five equals negative four. Negative four plus eight equals four. This graph should have a point at one, four.

Okay, let’s consider the point one, four. a goes through one, four. b does not go one- through one, four. And c does not go through one, four. b and c cannot graph this equation. Using a table, we’ve narrowed down the graph to a.

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