Question

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

Answer 1

Explained below

Explanation:

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.