To change how a quadratic function looks on a graph, we use something called translations. Let's take a look at the basic quadratic function, which is written as $f(x) = x^2$.

Vertical Translations

• To move the graph up, we add a number to the function. For example, when we write $g(x) = x^2 + 3$, it moves the graph up by 3 units.

• To move the graph down, we take away a number. For instance, $h(x) = x^2 - 2$ makes the graph go down by 2 units.

Horizontal Translations

• To move the graph to the right, we subtract a number from $x$. For example, $k(x) = (x - 4)^2$ shifts the graph to the right by 4 units.

• To move the graph to the left, we add a number. So, $m(x) = (x + 1)^2$ moves it to the left by 1 unit.

By imagining these movements, you can see how the graph changes position. Remember, these shifts don’t change the shape of the graph at all!