Math Is Fun Forum

angel_12

Member

Registered: 2007-06-07

Posts: 4

Solutions to quadratic equations when graphs are given..

Hi all,

can u ppl plz help me how to solve quadratic equations when graphs are given & when inequalities are there?

i seriously need that...i get so confused with those..plz do lemme know easy way to remember those...plz sirs & friends

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Nothing is impossible..even impossible says I'm possible!

yonski

Member

Registered: 2005-12-14

Posts: 67

Re: Solutions to quadratic equations when graphs are given..

I just think of the shape of the quadratic curve, so x^2 curves are 'valley shaped' and -(x)^2 curves are 'hill shaped'.

If you're looking to solve say x^2 + 5x + 6 < 0 , then you first factorise to give (x+3)(x+2) < 0 .

Now you know that the curve is valley shaped, and you're looking for the part of this that's below the x-axis. The factorised equation above gives the points that the curve crosses the x-axis, so the curve will be below the x-axis for all x values between these points. Therefore the solution is -3<x<-2 .

Say that instead of this you were looking for x^2 + 5x + 6 > 0 . Once again this factorises to give (x+3)(x+2) > 0 .

Now the inequality states that you're looking for the parts of the curve which are above the x-axis. So once again imagine the shape of the curve cutting the x-axis. This time it'll be > 0 when x<-3 or x>-2 .

Hopefully that helps somewhat, but the best way to learn is to keep doing lots of questions until it's drilled into your head!

Last edited by yonski (2007-06-07 04:57:56)

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Student: "What's a corollary?"
Lecturer: "What's a corollary? It's like when a theorem has a child. And names it corollary."

angel_12

Member

Registered: 2007-06-07

Posts: 4

Re: Solutions to quadratic equations when graphs are given..

Hey Yonski..Thanks a lot 4 ur reply!

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Nothing is impossible..even impossible says I'm possible!