So before we can decide which graph it is, we have to find the zeros (x-intercepts) of this graph. We can do this by setting y to 0.
Firstly, factor out 3x on the right side of the equation: [tex] 0=3x(\frac{x}{2}-2) [/tex]
Next, use the zero product property to solve y = 0:
[tex] 3x=0\\ x=0 [/tex]
[tex] \frac{x}{2}-2=0\\\\ \frac{x}{2}=2 \\ \\ x=4 [/tex]
So we know that the zeros of this equation are (4,0) and (0,0). Looking at the four graphs, the only graph that has a line crossing those 2 points is the first graph. Therefore, the graph of this equation is the first graph.
