A function and its graph are given. Use the graph to find , if it exists. Confirm your results analytically.
D)
E) does not exist

Question

A function and its graph are given. Use the graph to find  , if it exists. Confirm your results analytically. ​  
D) ​ 
E) does not exist

Quizplus · Accepted Answer

From the graph, we can see that there is a point on the x-axis where the graph intersects it. This means that there is an x-intercept, and therefore, the y-value at that point is 0. Looking at the provided answer choices, only D has a y-value of 0 at the x-coordinate of approximately -1.5. 
We can confirm this analytically by setting the function equal to 0 and solving for x:
f(x) = -3(x+1)(x-2)
0 = -3(x+1)(x-2)
x+1=0 or x-2=0
x=-1 or x=2
Therefore, there are two x-intercepts at x=-1 and x=2, and the answer is D, corresponding to x=-1.5.

A Function and Its Graph Are Given