Question

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 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 $(5,- 2)$. So, $h = 5$ and $k=-2$.

Step3: Find the value of $a$

We can use another point on the graph, say $(6,-4)$. Substitute $x = 6$, $y=-4$, $h = 5$ and $k = - 2$ into the equation $y=a(x - h)^4 + k$.
We get $-4=a(6 - 5)^4-2$.
Simplify the right - hand side: $-4=a\times1^4-2$, which is $-4=a - 2$.
Solve for $a$: $a=-4 + 2=-2$.

Answer:

$y=-2(x - 5)^4-2$