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The axis of symmetry is the line which divides the parabola into two symmetrical halves. It is given by the equation x = h. For example, the line of symmetry in the graph of y = (x - 2)2 + 1 is x = 2:

Axis of Symmetry

Graphing y = a(x - h)2 + k

In addition to shifting the parabola up, down, left, and right, we can stretch or shrink the parabola vertically by a constant. We can make a data table for the graph of y = 2x2:

Data Table for y = 2x2
Here, the y increases from the vertex by 2, 6, 10, 14,…; that is, by 2(1), 2(3), 2(5), 2(7),….

In general, in the graph of y = a(x - h) + k, as x increases or decreases by units of 1 starting from the vertex, y increases by 1a, 3a, 5a, 7a,….

Here is the graph of y = 2x2:

Graph of y = 2x2

Graphing y = - a(x - h)2 + k

Sometimes, the coefficient in front of (x - h) is negative. If this is the case, the parabola opens downward. In the graph of y = - a(x - h) + k, the vertex and axis of symmetry are still (h, k) and x = k, but as x increases or decreases by units of 1 starting from the vertex, ydecreases by 1a, 3a, 5a, 7a,….

For example, here are the data table and graph for y = - (x - 2)2 + 3:

Graph of y = - (x - 2)2 + 3

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