To write the equation in vertex form, we start with the general vertex form of a quadratic function, which is:
[tex]\[ g(x) = (x - h)^2 + k \][/tex]
Here, [tex]\((h, k)\)[/tex] represents the vertex of the function.
Given that the vertex of the function [tex]\(g(x)\)[/tex] is located at (9, 0), we can identify the values of [tex]\(h\)[/tex] and [tex]\(k\)[/tex] as follows:
1. The [tex]\(x\)[/tex]-coordinate of the vertex is 9. Therefore, [tex]\(h = 9\)[/tex].
2. The [tex]\(y\)[/tex]-coordinate of the vertex is 0. Therefore, [tex]\(k = 0\)[/tex].
With these values of [tex]\(h\)[/tex] and [tex]\(k\)[/tex], we can substitute them back into the vertex form equation:
[tex]\[ g(x) = (x - 9)^2 + 0 \][/tex]
Simplifying the equation, we get:
[tex]\[ g(x) = (x - 9)^2 \][/tex]
In conclusion, the values are:
- [tex]\(h = 9\)[/tex]
- [tex]\(k = 0\)[/tex]
So, the equation in vertex form is:
[tex]\[ g(x) = (x - 9)^2 + 0 \][/tex]
Which simplifies further to:
[tex]\[ g(x) = (x - 9)^2 \][/tex]
