Sarah graphs the equations y=1/4 x^2 and y=-1/2 x+2 to solve the equation 1/4 x^2=-1/2 x+2 Her graph is shown below
What are the solutions?
Describe how you found your solution(s) on the graph using a complete sentence.

x = -4, 2

Step-by-step explanation:

¼x² = -½x + 2

x² + 2x - 8 = 0

x² + 4x - 2x - 8 = 0

x(x + 4) - 2(x + 4) = 0

(x + 4)(x - 2) = 0

x = 2, -4

On the graph, the solutions are the x-coordinates of the points of intersection

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.