Question

fill in the equation for this function. y = ?(x - )^3 +

Explanation:

Step1: Identify the form of cubic - function

The general form of a cubic function is $y = a(x - h)^3 + k$, where $(h,k)$ is the vertex of the cubic function.

Step2: Locate the vertex

From the graph, the vertex of the cubic function is at the point $(0, - 2)$. So, $h = 0$ and $k=-2$.

Step3: Find the value of \(a\)

We know the function passes through the point $(1,2)$. Substitute $x = 1$, $y = 2$, $h = 0$ and $k=-2$ into $y=a(x - h)^3 + k$. We get $2=a(1 - 0)^3-2$.

Step4: Solve for \(a\)

First, simplify the equation $2=a - 2$. Then add 2 to both sides of the equation: $a=4$.

Answer:

$y = 4(x - 0)^3-2$