fill in the equation for this function. y = ?(x - )^4+

Explanation:

Step1: Identify the vertex form of a quartic function

The general form of a quartic function in vertex - form is $y = a(x - h)^4 + k$, where $(h,k)$ is the vertex of the function.

Step2: Determine the vertex of the function from the graph

The vertex of the given graph is at the point $(0,0)$. So, $h = 0$ and $k = 0$.

Step3: Find the value of $a$

We can use another point on the graph, say $(1,3)$. Substitute $x = 1$, $y = 3$, $h = 0$ and $k = 0$ into $y=a(x - h)^4 + k$. We get $3=a(1 - 0)^4+0$, which simplifies to $3=a\times1^4$, so $a = 3$.

Answer:

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