Question

WITHOUT using a graphing device, find the x- and y-intercepts of the graph:y = 3x^3 - 9x^2

Answer 1

Given:

The function is,

`y=3x^3-9x^2`

To find the x intercept set y=0,

`\begin{gathered} y=3x^3-9x^2 \\ 3x^3-9x^2=0 \\ x^2(3x-9)=0 \\ \Rightarrow x^2=0,3x-9=0 \\ x=0,3x=9 \\ x=0,x=(9)/(3) \\ x=0,x=3 \end{gathered}`

So, x-intercepts are ( 0 , 0 ), ( 3, 0 ).

Now to find y-intercepts set x=0.

`\begin{gathered} y=3x^3-9x^2 \\ y=3(0)-9(0) \\ y=0 \end{gathered}`

y- intercept is ( 0 ,0 )

Answer: option e)