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  f(x) = (x +4)(x -1)(x -2)²

Step-by-step explanation:

The given points are all x-intercepts of the function. As such, each corresponds to a factor of the function. The x-intercept x=p corresponds to factor (x-p), for example.

Here, the x-intercept (2, 0) is repeated. It is said to have "multiplicity 2". That multiplicity value means the factor will have an exponent of 2 in the factored form of the function:

  f(x) = (x -(-4))(x -2)(x -1)(x -2)

  f(x) = (x +4)(x -1)(x -2)²

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Additional comment

When an x-intercept has even multiplicity, the graph will touch the axis there, but will not cross.

step-by-step explanation:

3+x

step-by-step explanation: