Question

How do you graph `y=3(x+3)^2 - 3`?

Answer 1

If you expand it you get `y=3x^2+18x+24`

Explanation:

With graph

graph{3x^2+18x+24 [-10, 10, -5, 5]}

Answer 2

See the explanation section.

Explanation:

For `y = a(x-h)^2 +k` the vertex is `(h,k)` and the graph opens from the vertex through the points `x = h +-1` and `y = k +a` That is, through the points `(h+1, k+a)` and `(h-1, k+a)`

For `y = 3(x+3)^2-3`, the vertex is `(-3,-3)` and with `a=3`, the parabola opens upward through the points `x= -3 +-1` and `y = -3+3 = 0`. That is, through the points `(-2,0)` and `(-4,0)`