Question

Begin by graphing the standard quadratic function, f(x) = x². Then use transformations of this graph to graph the given function. g(x) = (x − 2)²

Accepted Answer

Start by understanding the parent function, which is the standard quadratic function $$f(x) = x$$^{2}$$. This graph is a parabola with its vertex at the origin (0$$,0)$$ and it opens upwards. Identify the given function g(x) = (x$$ - $$2)^{2}. $$Notice that it is in the form $$g(x) = (x - h$$)^{2}$$, where h = 2$. Recognize that the transformation from f(x$$)$$ to g(x$$)$$ involves a horizontal shift. Specifically, the graph of f(x$$)$$ is shifted to the right by 2 units because of the (x - 2$$)$$ inside the square. To graph g(x$$)$$, take the graph of f(x$$) = $$x^{2}$$ and move every point 2 units to the right. The vertex of $$g(x)$$ will now be at $$(2, 0)$$ instead of $$(0, 0). $$Check a few points to confirm the transformation: for example, when $$x = 2$$, $$g(2) = (2 - 2$$)^{2}$$ = 0$$, which matches the new vertex. Plot these points to complete the graph.

Begin by graphing the standard quadratic function, f(x) = x². Then use transformations of this graph to graph the given function. g(x) = (x − 2)²

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Key Concepts

Standard Quadratic Function

Horizontal Shifts of Functions

Graph Transformations