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## Algebra (all content)

### Unit 9: Lesson 12

Sal solves a few quadratic inequalities by moving all terms to one side of the inequality and graphing the resulting expression. Created by Sal Khan.

## Want to join the conversation?

• What does it meant at ?? What is the point on the curve?
• At , Sal highlites the curve under the x-axis, but remember that the entire curve is f(X) (which is also called y). Since you're dealing with a curve rather than a straight line, you use f(x). A straight line is simple, so y works, but curves are more complicated and f(x) is a more advanced tool. Keep it up and you'll gradually understand. It takes time and practice, but it's worth it.
• Why is the y intercept -6? Sal mentions it at
• Because, like in y=mx+b, the constant term is the y-intercept.
• How do you solve this inequality x^2+3x is greater or equal to -2. I've tried doing it and got x is greater or equals to -2 and x is greater or equals to -1 but that is no the right answer. Please help
• `x² + 3x ≥ -2`
`=> x² + 3x + 2 ≥ 0`
`=> x² + 2x + x + 2 ≥ 0`
`=> x(x + 2) + 1(x + 2) ≥ 0`
`=> (x + 1)(x + 2) ≥ 0`
`=> x ∈ [-∞, -2]⋃[-1, ∞]`

Stated simply, `x < -2` or `x > -1`.
• Why is F(x)>0??? I thought F(x) is changed into 0? So,how can F(x)>0?? Confusing.
• In solving quadratic equalities Sal was showing how to solve for f(x) = 0. Meaning the points at which the f(x) line crosses or intersects the x-axis (=0). In solving quadratic INequalities Sal shows how you can solve for f(x) > 0 or f(x) < 0. Meaning the x coordinates at which point the f(x) line is above (>) or below (<) the x-axis (0).

The two are related because the points where the f(x) line intersect the x-axis (=0) are also the same points between which the f(x) line rises above (>) or falls below (<) the x-axis (0).
• Why does he put the vertex of the parabola on the y-axis? Shouldn't it be @ (-0.5,-6.25)? Or is he just making a rough drawing... not intentional?
• Do you think that graph can be misleading especially to those who are beginner. From my point of view it looks like that the vertex is (0, -6)
(1 vote)
• Why do you have to change the sign > to <?? It looks something like you change both sides equations...but instead of doing that,you change the signs? Why not use = instead of </>?(at )

• I use a simple example whenever I can.
Say 10>0. If you change the sign on 10, then -10<0.
The same exact change happens if there are multiple numbers, as long as you change all of the signs.
BTW, if you have numbers on both sides of inequality, say, 10>9, you just change signs on both sides and flip the arrow. -10<-9. Hope this helps.
• I dont understand how to graph Y >X^2+4
• Also, when an inequality is solved for y, you can interpret "y >" as "above the line" and "y <" as "below the line". Just be careful, as a negative coefficient will reverse this logic. When in doubt, test points!
• What point is the axis of symmetry?
• the axis of symmetry is the line that goes through the vertex. hope this helps! :-)