Solve 2x2 + 12x − 14 = 0 by completing the square, options: a. 2(x + 6)2 = 26; x = −6 + square root 13, x = −6 − square root 13 b. 2(x + 6)2 = 20; x = −6 + square root 20, x = −6 − square root 20 c. 2(x + 3)2 = 32; x = 1, x = −7 d. 2(x + 3)2 = 32; x = 13, x = 19

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.