The equation of the parabola f(x) = x² is transformed right 2, up 3, to make another parabola of the equation g(x) = (x - 2)² + 3. Hence, the first option is the right choice.
The process of modifying an existing graph, or graphed equation, to generate a version of the following graph is known as graph transformation.
If the equation of the original graph is f(x) and the transformed graph is g(x), such that g(x) = f(x + p) + q, then the graph of g(x) is p units left and q units up from f(x).
In the question, we are given the equations of the parabolas f(x) = x² and g(x) = (x - 2)² + 3, where f(x) is transformed to make g(x).
We are asked to identify the transformation from f(x) to g(x).
The equation of g(x) = (x - 2)² + 3, in terms of f(x) = x² can be written as
g(x) = f(x- 2) + 3, which is of the form g(x) = f(x + p) + q, where the graph of g(x) is transformed from f(x) by moving it p units left and q units right.
So, we can say that f(x) = x² is moved 2 units right and 3 units up to form g(x) = (x - 2)² + 3.
∴ The equation of the parabola f(x) = x² is transformed right 2, up 3, to make another parabola of the equation g(x) = (x - 2)² + 3. Hence, the first option is the right choice.
Learn more about the transformation of graphs at
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