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

Jul 11, 2017

Explained below

#### Explanation:

The given function is horizontal and vertical transformation of parabola $y = 3 {x}^{2}$, 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.