Video: Approximating Roots of Quadratic Equations with a Graphing Calculator

Using the given graph of the equation 𝑦 = π‘₯Β² + 2π‘₯ βˆ’ 5, find which of the following is the best approximation for the solutions to π‘₯Β² + 2π‘₯ βˆ’ 5 = 0. [A] π‘₯ = βˆ’3 or 1 [B] π‘₯ = βˆ’3.5 or 1.5 [C] π‘₯ = βˆ’4 or 2

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Video Transcript

Using the given graph of the equation 𝑦 equals π‘₯ squared plus two π‘₯ minus five, find which of the following is the best approximation for the solutions to π‘₯ squared plus two π‘₯ minus five equals zero. The answers are A) π‘₯ is equal to negative three or one. B) π‘₯ is equal to negative 3.5 or 1.5. Or C) π‘₯ is equal to negative four or two.

Well, to solve this problem, we want to see where our graph has a 𝑦-value equal to zero. And that’s because we want to find solutions to π‘₯ squared plus two π‘₯ minus five is equal to zero. And if we take a look at our graph, we’re gonna see that there’re two points where this occurs.

Now to find the π‘₯-values of these two points, so the solution to approximation for the solutions, we need to be able to read off what values they are. And to do that, we need to know what is the scale of our graph. We can see the scale is one square is equal to 0.5. So therefore, we can see that the two values we can get from our graph are going to be negative 3.5 and 1.5.

So therefore, the best approximation for the solutions to π‘₯ squared plus two π‘₯ minus five equals zero is going to be B. And that’s π‘₯ equals negative 3.5 or 1.5. And this is the case because these are the two points where our graph crosses the π‘₯-axis, so therefore where 𝑦 would be equal to zero.

And if we take a look at the other two options, we could see that C would be too great. So the values are actually bigger than the values that we would get if we crossed the π‘₯-axis on our graph. And A would give us values that are too small because you could see that these are less than the values that we get if we found the point where the graph crosses the π‘₯-axis.

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