If these statements are true: x+2y=0 and 4x=-8y-2, which, if any, is a point on the graphs? (4, -2), (4, -1)?

Answer 1

you plug in the points into the equations
(4,-2) for x+2y=0 4x=-8y-2
4+2(-2)=4-4=0(true) 4(4)=-8(-2)-2
16=16-2=14(not true)

(4,-1) for x+2y=0
4-2=0
2=0(not true)
None of these two points are on the graph

Answer 2

from x² + 4x + 4 = 8y + 4 you get (x + 2)² = 8(y + ½) it quite is one general sort, from which you examine the vertex as (-2, -½), and the focal length as 8/4 = 2. extra useful for graphing is (a million/8)(x + 2)² = (y + ½) the place the a million/8 is the vertical stretch (decrease to that end) plot the vertex, then pass 2 left and suitable from there and particularly of going up 2² = 4, pass up (a million/8)(4) = ½. from the vertex pass 4 left and suitable and particularly of going up 4² = sixteen pass up sixteen/8 = 2. very huge parabola.

Answer 3

x + 2y = 0
x = -2y

4(-2y) = -8y - 2
-8y = -8y - 2
0y = -2
y = -2/0
y = undefined

The 2 problems are parallel and therefore never intercept and have no solution.

Answer 4

ummmmm none of those