We have already discovered how to graph linear functions. But what does the graph of y = x2 look like? To find the answer, make a data table:
Note that the parabola does not have a constant slope. In fact, as x increases by 1, starting with x = 0, y increases by 1, 3, 5, 7, . As x decreases by 1, starting with x = 0, y again increases by 1, 3, 5, 7, .
In the graph of y = x2, the point (0, 0) is called the vertex. The vertex is the minimum point in a parabola that opens upward. In a parabola that opens downward, the vertex is the maximum point.
We can graph a parabola with a different vertex. Observe the graph of y = x2 + 3:
We can also shift the vertex left and right. Observe the graph of y = (x + 3)2:
In general, the vertex of the graph of y = (x - h)2 + k is (h, k). For example, the vertex of y = (x - 2)2 + 1 is (2, 1):