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A quadratic function y = f(x) is plotted on a graph and the vertex of the resulting

parabola is ( 3, -3 ). What is the vertex of the function defined as g(x) = -f (x – 3)

User Whoisearth
by
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1 Answer

3 votes

Answer:

The vertex of g(x) is (6,3).

Explanation:

Quadratic Function

The vertex form of the quadratic function has the following equation:


y=a(x-h)^2+k

Where (h, k) is the vertex of the parabola that results when plotting the function, and a is the leading coefficient.

We know a quadratic function y=f(x) is represented by a parabola whose vertex is at (3,-3). Substituting in the equation:


y=a(x-3)^2-3

The function g(x) is defined as:


g(x)=-f(x-3)

Substituting f(x):


g(x)=-[a(x-3-3)^2-3]

Operating:


g(x)=-a(x-6)^2+3

This function is represented by a parabola with its vertex at (6,3).

The vertex of g(x) is (6,3).

User Mhbdr
by
8.7k points

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