We have already discovered how to graph linear functions. But what does the graph of
y = x
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 = x 2 , 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 = x
2 + 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
. For example, the vertex of
y = (x - 2)2 + 1