Graphing y = x2

us have currently discovered how to graph straight functions. Yet what does the graph the y = x2 look like? To find the answer, do a data table:
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Data Table because that y = x2 and also graph the points, connecting them with a smooth curve:
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Graph that y = x2 The form of this graph is a parabola.

note that the parabola walk not have a consistent slope. In fact, as x rises by 1, starting with x = 0, y rises by 1, 3, 5, 7,…. As x to reduce by 1, starting with x = 0, y again boosts by 1, 3, 5, 7,….

Graphing y = (x - h)2 + k

In the graph the y = x2, the point (0, 0) is called the vertex. The crest is the minimum allude in a parabola that opens upward. In a parabola that opens downward, the vertex is the best point.

We can graph a parabola v a different vertex. Observe the graph the y = x2 + 3:

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Graph that y = x2 + 3 The graph is shifted up 3 systems from the graph that y = x2, and also the peak is (0, 3). Observe the graph the y = x2 - 3:
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Graph of y = x2 - 3 The graph is shifted under 3 devices from the graph of y = x2, and the peak is (0, - 3).

We deserve to also change the crest left and also right. Watch the graph the y = (x + 3)2:

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Graph the y = (x + 3)2 The graph is change left3 units from the graph the y = x2, and also the crest is (- 3, 0). Watch the graph that y = (x - 3)2:
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Graph the y = (x - 3)2 The graph is shifted to the right3 systems from the graph the y = x2, and the crest is (3, 0).


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In general, the peak of the graph the y = (x - h)2 + k is (h, k). Because that example, the peak of y = (x - 2)2 + 1 is (2, 1):

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Graph that y = (x - 2)2 + 1


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