What is the range of y equals 2x2 plus 4x-3?

Answer 1

y = 2x2 + 4x - 3

This equation describes a parabola. Because it's first term is positive, we know that it goes infinitely upward, and has a minimum that occurs at it's vertex. You can find it's vertex by taking it's derivative and solving for zero:

y' = 4x + 4

0 = 4x + 4

0 = x + 1

x = -1

y = (-1)2 + 4(-1) - 3

y = 1 - 4 - 3

y = -6

So the vertex is at (-1, -6), which means that y ≥ -6