f(x) = x^2 : How do you graph -3 (x-4)^2 +5

Question

This question deals with the transformations of graphs.

Answer 1

y = x^2 to y = -3(x-4)^2 + 5

We have 4 transformations: a horizontal shift from the -4, a vertical shift from the +5 and two from the -3.

The -3 tells us that the graph will be reflected across y =0 (i.e it will now be upside down) and also enlarged by a factor of 3. So originally f(2) = 2^2 = 4 now f(2) will equal -3(2)^2 or - 12

The -4 is a right shift or 4 units, so the vertex will move from (0,0) to (4,0)

The + 5 is a upwards shift of 5 units, so the vertex will again move but this time from (4,0) to (4,5)

Answer 2

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