Let’s analyze the given function [tex]\( g(x) = (x-9)^2 + \)[/tex].
### Step-by-Step Solution:
1. Understanding the Vertex Form:
The vertex form of a quadratic function is given by:
[tex]\[
g(x) = a(x-h)^2 + k
\][/tex]
Here, [tex]\((h, k)\)[/tex] represents the vertex of the parabola.
2. Identifying Components of the Function:
Observing the given function [tex]\( g(x) = (x-9)^2 \)[/tex], we can directly compare it with the vertex form [tex]\( g(x) = a(x-h)^2 + k \)[/tex].
- The term inside the parenthesis with [tex]\( x \)[/tex] (i.e., [tex]\((x - 9)\)[/tex]) provides the value of [tex]\( h \)[/tex]:
[tex]\[
h = 9
\][/tex]
- The constant term added outside the square term represents [tex]\( k \)[/tex]. Since no constant term is explicitly provided in the equation [tex]\( (x-9)^2 \)[/tex], we can infer that:
[tex]\[
k = 0
\][/tex]
3. Vertex of the Function:
From the values identified, the vertex of the function [tex]\( g(x) = (x-9)^2 \)[/tex] is:
[tex]\[
(h, k) = (9, 0)
\][/tex]
### Conclusion
The values of [tex]\( h \)[/tex] and [tex]\( k \)[/tex] are [tex]\( h = 9 \)[/tex] and [tex]\( k = 0 \)[/tex], respectively. Thus, the equation in vertex form is:
[tex]\[
g(x) = (x-9)^2 + 0
\][/tex]
