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The parent function of the function [tex]$g(x) = (x - h)^2 + k$[/tex] is [tex]$f(x) = x^2$[/tex]. The vertex of the function [tex][tex]$g(x)$[/tex][/tex] is located at [tex]$(9, -8)$[/tex]. What are the values of [tex]$h$[/tex] and [tex][tex]$k$[/tex][/tex]?

[tex]\[ g(x) = (x - \boxed{h})^2 + \boxed{k} \][/tex]

Sagot :

GinnyAnsweridn
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]
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