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

Explanation:

Step1: Identify the vertex form of a 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 graph.

Step2: Locate the vertex of the graph

From the graph, the vertex of the cubic function is at the point $(0, - 3)$. So, $h = 0$ and $k=-3$.

Step3: Find the value of (a)

We can use another point on the graph, say $(1, - 2)$. Substitute $x = 1$, $y=-2$, $h = 0$ and $k = - 3$ into the equation $y=a(x - h)^{3}+k$. We get $-2=a(1 - 0)^{3}-3$. Simplify the equation: $-2=a - 3$. Add 3 to both sides of the equation: $a=1$.

Answer:

$y = 1(x - 0)^{3}-3$