Using the vertex form of the quadratic equation, f(x) = (x - h)², let's examine a few more graphs. The variable, h, represents the x-value of the vertex. When the vertex moves left or right on the x-axis from the original vertex (0, 0) of the parent function, the value of h will tell you the direction and the distance of that move. Let's take a look at a few examples starting with the parent function f(x) = x².

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What if you wanted to move the graph 2 units to the right? The function would then become f(x) = (x - 2)². Remember to pay close attention to the subtraction sign in the original equation!

Take a look at the graph below. What do you think the third parabola's h is? Click the graph to see the correct answer.

The function moved 2 units to the left from the parent function. This gives us the new function f(x) = (x - (-2))² or f(x) = (x + 2)².

As you can see, the value of h determines the horizontal shift of the graph, also called horizontal translation.

• If h is positive, the graph moves h units to the right.
• If h is negative, the graph moves h units to the left.