What polynomial has a graph that passes through the given points? (-2, 2) (-1, -1) (1, 5) (3, 67) a. y = x4 + 4x3 + 2x2 - 2x b. y = -x3 + 4x2 + 2x - 2 c. y = x3 + 4x2 + 2x - 2 d. y = x3 - 4x2 - 2x - 2

Let's prove with x=1. The value of y is the sum of coefficients, and it would be 5

Option A. x=1, y=1+4+2-2→y=5  Ok
Option B. x=1, y=-1+4+2-2→y=3  No
Option C. x=1→y=1+4+2-2→y=5 Ok
Option D. x=1→y=1-4-2-2→y=-7  No

Then we have to options A or C

Let´s prove another point, for example (-1,-1), when x=-1, y=-1
Option A. x=-1→y=(-1)^4+4(-1)^3+2(-1)^2-2(-1)
y=1+4(-1)+2(1)+2=1-4+2+2→y=1 No

Option C. x=-1→y=(-1)^3+4(-1)^2+2(-1)-2
y=-1+4(1)-2-2=-1+4-2-2→y=-1 Ok

Option C. y=x^3+4x^2+2x-2  

Step-by-step explanation:

Set your compass to length say AB and draw a circle centre A, without adjusting the compass, draw another circle with centre B. Name their intersectin C and D, erase the other part of the circle and leave just the intersect C and D. Draw a circle with centre A that passes through the intersection C and D, also draw a straight line that passes through centre C and D. Make an intersection say E on the circle by puting your comass on C and D. Join C and D to this intersection E.