How do you sketch the graph of #y=-3(x+5)^2+1# and describe the transformation?

1 Answer
Jul 11, 2017

Explained below


The given function is horizontal and vertical transformation of parabola #y=3x^2#, opening up, as shown in the figure. Its axis if symmetry is y axis. Both branches of parabola would pass through points (1,3) and -1,3)

I. The first transformation is changing the sign of the term containing #x^2#. This would make the parabola open downwards.

II Second transformation is vertical shift 1 unit up

III Third transformation is horizontal shift by 5 units to the left.

The transformed parabola is also shown in the figure.

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