Question

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

Explanation:

Step1: Identify vertex form of 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

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

Step3: Find the value of $a$

We can use another point on the graph, say $(4,4)$. Substitute $x = 4$, $y = 4$, $h = 3$ and $k = 3$ into $y=a(x - h)^4+k$.
\[

$$\begin{align*} 4&=a(4 - 3)^4+3\\ 4&=a\times1^4+3\\ 4&=a + 3\\ a&=1 \end{align*}$$

\]

Answer:

$y = 1(x - 3)^4+3$