The curve has been attached and the answer choices are:

y = 3x² – 2x + 1

y = 3x² – 6x + 3

y = 3x²<span> – 7x + 1
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The attached graph has a vertex in the first quadrant. Therefore, the coordinates of the vertex would be both positive.

Let's start with first equation:

y = 3x² – 2x + 1

using the equation of axis:
x = -b/2a
x = 2/6
x = 1/3
SUbstituting the value of x in the main equation to get the y-coordinate of the vertex.
y = 3(1/3)² – 2(1/3) + 1
y = 3/9 – 2/3 + 1
y = 1/3 – 2/3 + 1
y = (1 - 2 + 3)/3
y = 2/3

Hence, the vertex would be:
(h,k) = (1/3 , 2/3)

Also, the leading coefficient is positive, so the parabola would be concave up.

Thus the final answer choice will be:

y = 3x² – 2x + 1