Question

How do you graph `f(x)=2(x+1)^2-2`?

Answer 1

Given -
y= 2`(x + 1)^2` - 2
Simplify it
y = 2 (`x^2` +2x + 1) -2
y = 2`x^2` + 4x +2 - 2
Its quadratic equation.
y = 2`x^2` + 4x
Find its vertex.
x = `(-b)/(2a)` = `(- 4)/(2 xx 2)` = - 1

At x = -1 ; the curve turns. Take a few points on either side.

Plot then and Join them.
graph{2x^2 + 4x [-11.13, 8.87, -4.16, 5.84]}

x y
-4 16
-3 6
-2 0
-1 -2
0 0
1 6
2 16