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The parent function of the function g(x) = (x – h)2 + k is f(x) = x2. The vertex of the function g(x) is located at (9, –8). What are the values of h and k?

g(x) = (x – )2 +

Respuesta :

[tex]\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} y=a(x- h)^2+ k\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k})\\\\ -------------------------------\\\\ \stackrel{\textit{its vertex is at 9, -8}}{g(x)=(x-\stackrel{h}{9})^2\stackrel{k}{-8}}\qquad \qquad \begin{cases} h=9\\ k=-8 \end{cases}[/tex]

Answer:

[tex]g(x) = (x - 9)^2-8[/tex]

Step-by-step explanation:

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 g(x) is located at (9, -8)

We are given with vertex that is the value of h and k

[tex](9,-8)[/tex] where  [tex]h=9[/tex] and [tex]k=-8[/tex]

[tex]g(x) = (x - h)^2+k[/tex]

Replace h and k values

[tex]g(x) = (x - 9)^2-8[/tex]

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