Question

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

Answer 1

To represent a cube root function with a turning point at (-2,3), one possible equation is f(x) = ∛(x + 2) + 3. This assumes the 'a' value, which determines the stretch or compression, is 1 since no further information is provided.

Step-by-step explanation:

The question pertains to finding the equation of a cube root function given a turning point. For a cube root function of the form f(x) = a∙∛(x - h) + k, where (‘h’, ‘k’) is the turning point, we can substitute the given turning point (-2, 3) into the equation to find the value of ‘a’.

Assuming the basic shape of the cube root function, we could start with the function f(x) = ∛(x + 2). However, this function would have the turning point (-2, 0), whereas we want the turning point to be (-2, 3). So, to shift the graph up 3 units, we add 3 to our function, yielding f(x) = ∛(x + 2) + 3. Since there's no information on the stretch or compression of the function, we can assume 'a' is 1.

Answer 2

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