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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 :

GinnyAnswer
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]
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