1Cademy - Example: Graphing $$f(x) = (x-5)^2$$

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Graphing a Quadratic Equation in Two Variables

Example

Example: Graphing $f(x) = (x-5)^2$

To graph a quadratic function with a horizontal shift, such as $f(x) = (x-5)^2$ , start by determining the value of $h$ . Since the function is in the form $f(x) = (x-h)^2$ , setting $x-5 = x-h$ reveals that $h = 5$ . Because $h > 0$ , this transformation shifts the basic parabola $f(x) = x^2$ horizontally to the right by $5$ units. By drawing the graph of $f(x) = x^2$ and translating every point rightward by $5$ units, you obtain the graph of $f(x) = (x-5)^2$ .