Sketch the graphs of the following

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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
b)y=4x-x2

Musaf,

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.

Penny

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