Question

Is the equation x^2+4x+3 greater than or equal to 0 positive in the interval (-infinity to -1)

Answer 1

\[{x}^2+4x+3 \ge 0\] \[ (-\infty, -1)\]

Answer 2

when x = -1, what do we get?

Answer 3

it follows the x^2 behaviour so its going to go positive at some point; so we should check it at -1 and maybe see where the vertex is

Answer 4

\[-6\ge0\]

Answer 5

at x=-1 i see it as equal to 0

Answer 6

oh sorry, yes..

Answer 7

and the vertex is at x = -b/2a; -4/2 = -2 so we havent reached the bottom of it at x=-1 yet

Answer 8

try x=-2 and see if its pos or neg

Answer 9

I don't know what is/how to do vertex this is just solving quadratric inequalities...

Answer 10

the vertex is where it bends at

Answer 11

I get neg with x=-2 but post with x=-4

Answer 12

well, since with x=-2 its negative; then we know that this contradicts the question and its false

Answer 13

we could also factor the poly and determine the zeros from that

Answer 14

I don't understand what you just said...

Answer 15

is -2 in our interval that they are concerned with?

Answer 16

I did that... and did a sign diagram but that interval is confusing so if any number in the interval give it negative and the other's make it positive which sign am i to choose positive or negative?

Answer 17

your spose to compare it to the question; if there is any value in the interval that is NOT 0 or above, the statement is false

Answer 18

since you found a value in the interval that is LESS than 0, the initial statement is false

Answer 19

I don't understand when am doing my sign chart/diagram... and I get 2 different signs for the values in my intervals then what am I suppose to do? Say that the statement is false?

Answer 20

http://www.wolframalpha.com/input/?i=x%5E2%2B4x%2B3

this kinda proves it as well

Answer 21

your sign values tell the sign of y

Answer 22

as you can see in the graph, from -1 to -3 we have a negative value

Answer 23

from -3 to -inf we have a positive value

Answer 24

since all the values along the interval are not greater than or equal to zero; the original statement is false

Answer 25

if I say that I have been taller than 5 feet all my life; and it turns out that I was once 3 feet tall; did i tell the truth or lie?

Answer 26

if i say that the values along the interval from -inf to -1 are positive values or 0

and some turn out to be negative values; is that statement true or false?

Answer 27

a lie... but I just realized that my interval is wrong because my zero's are wrong...

Answer 28

:) well, i only have to work with what you give me lol

Answer 29

yeah and you did a great job, thanks!!!

Answer 30

good luck ;)

Answer 31

thank you :)