Question

Using this picture, describe what we are doing with the factored form of p(x) shown in the image in order to create a sketch of the function.

Answer 1

Given:

`p(x)=(x-1)(x+1)(x-4)^2`

Sol:

`\begin{gathered} p(x)=(x-1)(x+1)(x-4)^2 \\ \\ p(0)=(0-1)(0+1)(0-4)^2 \\ \\ p(0)=-16 \end{gathered}`

X-intercept is at p(x) = 0 then,

`\begin{gathered} p(x)=0 \\ \\ p(x)=(x-1)(x+1)(x-4)^2 \\ \\ 0=(x-1)(x+1)(x-4)^2 \\ \\ x=-1,1,4 \end{gathered}`

At y- intercept the value of x is zero and at x = 0 function value is:

`\begin{gathered} y=-16 \\ \\ \text{ The point is:} \\ (0,-16) \end{gathered}`

At x-intercept y value is zero and x-intercept is -1,1,4 is:

`\begin{gathered} \text{ At }x=-1 \\ \\ the\text{ value of }y=0 \\ \\ (-1,0) \\ \\ At\text{ }x=1 \\ \\ \text{ The value of }y=0 \\ \\ (1,0) \\ \\ \text{ At }x=4 \\ \\ \text{ The value of }y=0 \\ \\ (4,0) \end{gathered}`

So all point is (-1,0) ,(1,0) and (4,0)