A quadratic function y, equals, f, of, xy=f(x) is plotted on a graph and the vertex of the resulting parabola is left bracket, 5, comma, 6, right bracket(5,6). What is the vertex of the function defined as g, of, x, equals, f, of, x, plus, 3, minus, 2g(x)=f(x+3)−2?

The vertex of the function g(x) = f(x + 3) − 2 is found by shifting the vertex of the original function f(x) three units to the left and then down two units:

Vertex of g(x) = (x - 3, y - 2) = (5 - 3, 6 - 2) = (2, 4)

Therefore, the vertex of g(x) is (2,4).

Answer Link

msm555 msm555 · Answer 2 · 2024-02-22T04:56:45+01:00

Answer:

[tex](2, 4)[/tex]

Step-by-step explanation:

Given that the vertex of the quadratic function [tex]y = f(x)[/tex] is (5, 6), the vertex form of a quadratic function is:

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

where

(h, k) is the vertex.

From the given information, we have:

[tex] f(x) = a(x - 5)^2 + 6 [/tex]

Now, we want to find the vertex of the function [tex]g(x) = f(x + 3) - 2[/tex].

Substitute [tex]x + 3[/tex] for [tex]x[/tex] in the vertex form of [tex]f(x)[/tex]:

[tex] g(x) = a((x + 3) - 5)^2 + 6 - 2 [/tex]

Simplify the expression:

[tex] g(x) = a(x - 2)^2 + 4 [/tex]

Comparing with vertex form; we get

h = 2 and k = 4

So, the vertex of [tex]g(x)[/tex] is [tex](2, 4)[/tex].