Question

Which of the following represents the graph of y = x3 - 2x2 - 5x + 6?

Answer 1

Hi there!
We are asked to find the graph that represents the cubic function y = x³ - 2x² - 5x + 6. To do this, we have to find the roots of the function, and we can do that by using the Rational Root Theorem, which is basically constant over the leading coefficient.
+ 6 / + 1
Now, just list all the factors of 6 and replace that as the numerators.
Factors: 1, 2, 3, 6
+1, +2, +3, +6 / +1
Now, just simplify for each one. We get the possible roots: 1, -1, 2, -2, 3, -3, 6, -6. All we have to do now is plug each one back into the equation and see which ones turn out to evaluate the function to zero. After doing so, we get the roots 1, -2, and 3. Now, look for the graph that has x-intercepts of 1, -2, and 3, and the only graph that works is Graph B. Therefore, the graph that represents the function y = x³ - 2x² - 5x + 6 is Graph B. Hope this helps and have a marvelous day!