Question

Which equation could generate the curve in the graph below

Answer 1

The curve has been attached and the answer choices are:

y = 3x² – 2x + 1

y = 3x² – 6x + 3

y = 3x² – 7x + 1

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