Question

If g(x) = x2 - 2x - 8, solve g(x) ≤ 0

Answer 1

Hmm... Wanna learn how to do this?

Answer 2

yes

Answer 3

We can make it 'less scary' by changing g(x) to y.

Answer 4

so, y = x^2 -2x -8

We want y to equal less than or equal to 0.

Answer 5

Do you know how to factor this?

Answer 6

As in how to factor y = x2 - 2x - 8 ?

Answer 7

(x+2)(x-4)

Answer 8

yes

Answer 9

Perfect!
Now, next question: What shape is this equation?

Answer 10

idk :(

Answer 11

Not a problem! Just remember: if you have x^2 in your equation, what will it be? A line? A circle? A square? A parabola? A triangle?

Answer 12

a parabola

Answer 13

{x|-2 ≤ x ≤ 4}; [-2, 4]

Answer 14

perfect! Now, is our parabola shaped more like a U (opening up) or a ^ (opening down)?

Answer 15

And yeah, that is our answer, but do you know *why*?

Answer 16

Hint: to remember if a parabola is going up or down, look at the sign in front of the x^2

Answer 17

down because of the nagative???

Answer 18

g(x) = x2 - 2x - 8

Answer 19

That was our original question.

Answer 20

So is there a positive or a negative in front of the x squared?

Answer 21

so its facing up

Answer 22

Perfect! And when you factored as (x-4)(x+2), where does that mean we place our points on the graph?

Answer 23

Hint:
it's (x-4)(x+2)=0 where the y is 0

Answer 24

x=4 so 4,0
x=-2 so -2,0???

Answer 25

That's right!

Answer 26

Now, here's where we solve: where on the graph is the line below y = 0?
Here's a picture of it: http://www.wolframalpha.com/input/?i=g%28x%29+%3D+x^2+-+2x+-+8

Answer 27

(That's why I asked for the direction of the graph. If it was upside down, our answer would be totally different)

Answer 28

thank you so much . i apreciate that you helped me understand

Answer 29

No problemo! Feel free to 'fan' me if you want to find me easily for future help! I like walking folks through to let them find answers on their own like this. :P

Answer 30

Yay! A new fan.