I need help for this question.

  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

_____

Additional comment

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

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.