Question

Which graph represents this equation?y = 3:2 - 61ОА.+X-4No26-24-6B.24N- 2C.

Answer 1

To determine which one is the graph of the equation:

`y=(3)/(2)x^2-6x`

We can finc the x-intercepts of the equations, we know that this happens when y=0, then we have:

`(3)/(2)x^2-6x=0`

Solving for x we have:

`\begin{gathered} (3)/(2)x^2-6x=0 \\ x((3)/(2)x-6)=0 \\ \text{then} \\ x=0 \\ or \\ (3)/(2)x-6=0 \\ (3)/(2)x=6 \\ x=(2)/(3)\cdot6 \\ x=4 \end{gathered}`

This means that the the graph have to cross the x axis in the values x=0 and x=4.

Looking at the options we notice that the only graph that do this is option B, therefore the gaprh of the equation is shown on B.