Question

A cube root function has a turning point located at (-2,3). Write an equation that could represent this function

Answer 1

Answer:

f(x) = A*∛(x + 2) + 3

Step-by-step explanation:

Suppose a generic cube as:

f(x) = A*∛(x - b) + C

We will have a turning point at the x value:

x = b

Then if we have a turning point at (-2, 3)

This means that the turning point is at x = -2 and y = 3

Then b = -2

And our cube root function will be something like:

f(x) = A*∛(x - (-2)) + C

f(x) = A*∛(x + 2) + C

And we know that f(-2) = 3

then:

f(-2) = A*∛(-2 + 2) + C = 3

f(-2) =  A*∛(0) + C = 3

      = C = 3

Then the general equation will be something like:

f(x) = A*∛(x + 2) + 3