Which equation could generate the curve in the graph below?
y = 3x2 – 2x + 1
y = 3x2 – 6x + 3
y = 3x2 – 7x + 1
y = 3x2 – 4x – 2

The only equation that has the vertex up the x-axis and, consequently, does not touch the x-axis is the first one: y = 3x^2 -2x+1.

Then, that is the answer.

To verify that you can calculate the discriminant, b^2 - 4(a)(c), for each equation and use these facts:

If b^2 - 4(a)(c) = 0, there is only one real root (the graph touches the x-axis in one point)

If b^2 - 4ac > 0, there are two real roots (the graph touches the x-axis in two different points)

If b2 - 4ac < 0, there are no real roots (the graph does not touch the x-axis). This is the case for y = 3x^2 - 2x + 1. (-2)^2 -4(3)(1) = 4 - 12 = -8 < 0 => not real roots.