Question

Determine whether a quadratic model exists for the set of values below. If​ so, write the model. f(0) = -4, f(3) = -19, f(-1) = -11

Select the correct choice below​:

A) A quadratic model does exist. It is ​f(x)= ?
B) A quadratic model does not exist.

Answer 1

A) The model exists: f(x) = -3x^2 +4x -4

Explanation:

A quadratic model will always exist for 3 given points, provided they are not on a line. In that case, a linear model is appropriate.

Here, the slope between -1 and 0 is positive, and the slope between 0 and 3 is negative. Thus, we know these points are not collinear, and a model must exist.

The model is most easily found using a quadratic regression tool. Such is shown in the attachment. It tells us that ...

f(x) = -3x^2 +4x -4