Math CentralQuandaries & Queries


Question from musaf, a student:

without detailed plotting of points,sketch the graphs of the following showing relevant information on the graphs:
a) y=(x-3)2 +5


I assume these are

a) y= (x - 3)2 + 5
b) y = 4x - x2

I can help you get started on a).

Sketch the graph of y = x2. Where is the vertex?

For the graph of y = (x - 3)2 the vertex has shifted over to x = 3. Sketch its graph.

Finally consider y = (x - 3)2 + 5. The relationship between this and the previous expression y = (x - 3)2 is that 5 has been added to each y-value, that is the graph has been shifted upwards 5 units. Sketch its graph.


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