Question

 Please help, Select the graph of the equation below. y=3/2x^2-6x.

Answer 1

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: $0=3x(\frac{x}{2}-2)$

Next, use the zero product property to solve y = 0:

$3x=0\\ x=0$

$\frac{x}{2}-2=0\\\\ \frac{x}{2}=2 \\ \\ x=4$

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.