Question

Help me graph an inequality (picture) PLEASE

Answer 1

@thomaster @agent0smith @ganeshie8

Answer 2

an absolute value you mean? all I see there is \(\bf f(x) = -\cfrac{1}{2}|x+2|+6\)

Answer 3

yess

Answer 4

well, is an absolute value, so pretty much all you need is the vertex
and to know that it has a negative in front of the expression, so it's going DOWNWARDS

then just pick 2 points, one to the left of the vertex, and one to the right of it, and draw the lines from the vertex to those points

Answer 5

what value of "x" will make the |x+2| to 0?

Answer 6

-2? and okay so it's a 1/2 compression, reflection, 2 left and 6 down?

Answer 7

and vertex is 2,6

Answer 8

\(\bf f(x) = -\cfrac{1}{2}|x+2|+6\\
f(x) = -\cfrac{1}{2}|(\color{red}{-2})+2|\color{red}{+6}\\
(\color{red}{-2, 6}) \Leftarrow vertex\)

Answer 9

and what do i do next?

Answer 10

then just pick 2 points on either side of the vertex for "x", then get "y", that'll give you a point on each side, and draw a line to them from the vertex

Answer 11

i need to fill in the chart that's in the picture above

Answer 12

a point on either side that is

say our vertex is (-2, 6) so say.... x = -5 and x = 9

Answer 13

well, then they want 5 points, so...you really only need 2 btw for the graph, but sure, pick 3 more if you want, the line will still go through them

Answer 14

okay so i wanna use for x: -2, -1, 0, 1, 2 and for y i put 2, 1, 0, 1, 2

Answer 15

hmm... vertex is (-2, 6)

well, you need at least one to the left of -2 and one to the right of -2

Answer 16

and then i need to use the "directions" for the equation which is a compression, 2 left and 6up

Answer 17

Okay I get it!! thanks!!

Answer 18

well... yes and no
if you use the points, the points will automatically will give the compression
as far as the shifting left and up, that's already done by the vertex

Answer 19

say lemme use ... x = -4 and x= 0

\(\bf x = -4\\
f(x) = -\cfrac{1}{2}|x+2|+6 \implies f(x) = -\cfrac{1}{2}|-4+2|+6 \implies y = 5\\
x = 0\\
f(x) = -\cfrac{1}{2}|x+2|+6 \implies f(x) = -\cfrac{1}{2}|0+2|+6 \implies y = 5\


so (-4, 5) and (0, 5)

Answer 20

ahh chucks.... lemme redo that

Answer 21

say lemme use ... x = -4 and x= 0

\(\bf x = -4\\
f(x) = -\cfrac{1}{2}|x+2|+6 \implies f(x) = -\cfrac{1}{2}|-4+2|+6 \implies y = 5\\
x = 0\\
f(x) = -\cfrac{1}{2}|x+2|+6 \implies f(x) = -\cfrac{1}{2}|0+2|+6 \implies y = 5\)


so (-4, 5) and (0, 5)

Answer 22

okay thank you!! so i can just pick out random points?

Answer 23

yes, any others will fall in that line