Sure, let's find the values of [tex]\( h \)[/tex] and [tex]\( k \)[/tex] needed to complete the equation [tex]\( g(x) = (x - h)^2 + k \)[/tex].
Given that the vertex of the function [tex]\( g(x) \)[/tex] is located at [tex]\( (9, -8) \)[/tex]:
1. Identify the Vertex Form:
The vertex form of a quadratic function is given by [tex]\( g(x) = (x - h)^2 + k \)[/tex], where [tex]\( (h, k) \)[/tex] is the vertex of the parabola.
2. Given Vertex:
The vertex of the function [tex]\( g(x) \)[/tex] is provided as [tex]\( (9, -8) \)[/tex].
3. Extracting Values:
From the given vertex [tex]\( (9, -8) \)[/tex]:
- [tex]\( h = 9 \)[/tex]
- [tex]\( k = -8 \)[/tex]
Therefore, by substituting these values into the vertex form of the quadratic equation [tex]\( g(x) = (x - h)^2 + k \)[/tex], we obtain:
[tex]\[ g(x) = (x - 9)^2 - 8 \][/tex]
So, the values of [tex]\( h \)[/tex] and [tex]\( k \)[/tex] are:
- [tex]\( h = 9 \)[/tex]
- [tex]\( k = -8 \)[/tex]
Thus, the complete function is:
[tex]\[ g(x) = (x - 9)^2 - 8 \][/tex]
And filling in the blanks in the form [tex]\( g(x) = (x - \square)^2 + \square \)[/tex]:
[tex]\[ g(x) = (x - 9)^2 + (-8) \][/tex]
