Which of the Following equation describes the graph?
A. [tex]y = \frac{1}{3} x ^{2} - x - 2[/tex] B. [tex]y = \frac{1}{3} x ^{2} - x + 2[/tex] C. [tex]y = - \frac{1}{2} x ^{2} - x - 2[/tex] D. [tex]y = \frac{1}{2} x ^{2} - x + 2[/tex]
We can eliminate choice C because our parabola is not upside down. The way I determined which one it was was by picking a point on the graph and testing the x value of the point in the equation. If the y value on the graph was the same as the y value on my calculator, then I chose the right one. Let me give you an example of what doesn't work first. Let's pick (3, 2) from the graph. Let's test that point in choice D. Filling in x = 3, y should = 2 if that's the right equation. [tex] \frac{1}{2}(3^2)-3+2= \frac{7}{2} [/tex]. Our y coordinate is not 7/2, it's 2. Let's try A: [tex] \frac{1}{3}(3^2)-3-2=-2 [/tex]. Again, our y value is 2, not -2. Let's try B: [tex] \frac{1}{3}(3^2)-3+2=2 [/tex]. See how that works? Your choice is B.
