Bellshaffonidn
Answered

IDNLearn.com offers a unique blend of expert answers and community-driven knowledge. Discover thorough and trustworthy answers from our community of knowledgeable professionals, tailored to meet your specific needs.

Writing an Equation in Vertex Form

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]\( g(x) \)[/tex] is located at (9, k). What are the values of [tex]\( h \)[/tex] and [tex]\( k \)[/tex]?

[tex]\[ g(x) = (x - \square)^2 + \square \][/tex]

[tex]\[ \square = \text{h} \][/tex]
[tex]\[ \square = \text{k} \][/tex]

Sagot :

GinnyAnsweridn
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]
We are delighted to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and see you next time for more reliable information.