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The function f(x) = x^2 was transformed to create the function g(x)=f(x-3)-4. What are the coordinates of the vertex of the gra...Question
the function f(x)=x² was transformed to create the function g(x)=f(x-3)-4. what are the coordinates of the vertex of the graph g?
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GPT 3.5
To find the vertex of the graph of g(x), we need to find the x-coordinate of the vertex first.
The function g(x) = f(x-3) - 4 shifts the function f(x) = x^2 3 units to the right and 4 units down.
The vertex of the original function f(x) = x^2 is at (0,0).
So, the vertex of g(x) = f(x-3) - 4 will be at (3, -4) since the function is shifted 3 units to the right and 4 units down.
Therefore, the coordinates of the vertex of the graph g are (3, -4).
The function g(x) = f(x-3) - 4 shifts the function f(x) = x^2 3 units to the right and 4 units down.
The vertex of the original function f(x) = x^2 is at (0,0).
So, the vertex of g(x) = f(x-3) - 4 will be at (3, -4) since the function is shifted 3 units to the right and 4 units down.
Therefore, the coordinates of the vertex of the graph g are (3, -4).
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