Question

Which of the following are true about the graph of y = (x - a)(x - b)2(x - c)3I) The graph travels through the point x = aII) The graph "bounces off" the point x = bIII) The graph "bounces off" the point x = c

Answer 1

Consider the given equation,

`y=(x-a)(x-b)^2(x-c)^3`

Put x = a in the equation,

`\begin{gathered} y=(a-a)(a-b)^2(a-c)^3 \\ y=(0)(a-b)^2(a-c)^3 \\ y=0 \end{gathered}`

So the graph of the function passes through (a,0), which is a valid point.

So, option (I) is correct.

Similarly, when substituting the other values, it is obtained that the curve of the given function passes through points (b,0) and (c,0).

But this contradicts with the statements in (II) and (III) respectively.

Therefore, it can be concluded that only statement (I) is correct.