View Full Version : Quadrtic equations and quadratic formulas
oscarlicous
May 8, 2009, 05:54 AM
this is kind of a dumb question, but I need help before my core 40 test. I was wondering how you do the equations and formulas? My teacher isn't the most helpful, but he tries to help with what ever I need in algebra. I don't really understands it so I was wondering if all you smart peopl could help this small minded person figure out quadratic equations?
thanks so much!! :)
galactus
May 8, 2009, 06:02 AM
Post something in particular. It is a broad subject.
oscarlicous
May 8, 2009, 07:51 AM
I don't understand the fromula part of the problem.
galactus
May 8, 2009, 07:53 AM
You mean ax^{2}+bx+c?
A quadratic equation describes a parabola.
oscarlicous
May 8, 2009, 08:16 AM
Like this http://www.mathwarehouse.com/quadratic/images/quadratic-formula-example.gif
galactus
May 8, 2009, 10:52 AM
That is the quadratic formula. That is one of the ways we solve quadratics(others being factoring and completing the square).
You just use the general formula:
x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a} to find your x values that make the quadratic equal 0. Those are called the roots or zeros of the quadratic.
a is the number in front of x^2, b is the number in front of x and c is the constant at the end.
These are called coefficients.
Example:
Suppose we had 2x^{2}+5x-6=0
a=2, b=5, c=-6
Plug them into the quad formula:
x=\frac{-5+\sqrt{5^{2}-4(2)(-6)}}{2(2)}=\frac{\sqrt{73}-5}{4}\approx .886
Now do the 'minus' case:
x=\frac{-5-\sqrt{5^{2}-4(2)(-6)}}{2(2)}=\frac{5-\sqrt{73}}{4}\approx -3.386
You have to do the two cases because a quadratic has two solutions.
See better now? It's just plug and chug.
From looking at your example, your quadratic was x^{2}+2x+1=0
Using the formula gives one solution of multiplicity 2. That is, x=-1 occurs in both cases.
That means even though a quadratic has two solutions, some have the same solution for both cases. That is called multiplicity.
Don't let it confuse you. Sometimes it happens that way.
There is also a thing called a 'discriminant'. b^{2}-4ac
See? That is the part inside the radical. We can use that to find out what sort of solutions it has.
For your x^{2}+2x+1, the discriminant is 2^{2}-4(1)(1)=0
When the discriminant equals 0, we have one solution of multiplicity 2. As we showed for that one. It's solution was -1 that occurred twice.
Also, if the discriminant is less than 0, then it has no real roots. Both solutions are complex. That happens when 4ac is bigger than b^2.
If the discriminant is greater than 0, then it has two real and unequal roots. Like the first one I showed you.
There. Is that a nice tutorial on quadratics or what? :)
oscarlicous
May 8, 2009, 01:56 PM
Yes it was! And thank you so much! That cleared everything up for me!
mathslover
May 9, 2009, 09:18 AM
This post is intended to help, and I certainly hope I don't confuse you further!
If asked to do a sketch of any quadratic curve, there are 3 types in general.
1) It cuts the x-axis at 2 different points. This happens when b^2-4ac > 0, or as galactus mentioned above, it has 2 real and unequal roots. The points where the curve and the x-axis meet would be the roots.
2) It exactly slides along the x-axis (i.e. turns just when it touches the axis). This happens when b^2-4ac = 0. It will have 2 real repeated roots that occur exactly where the curve touches the x-axis.
3) It does not touch the x-axis at all (i.e. either entirely on top or entirely at the bottom). This happens when b^2-4ac < 0. It will have no real roots.
The quadratic curve can also either turn up (smiling mouth) or down (frowning mouth).
It turns UP when the coefficient of x^2 is more than 0 (or a>0). The larger a is, the narrower your curve will be (i.e. the 2 upturned sides will be closer to each other).
It turns DOWN when the coefficient of x^2 is less than 0 (or a<0). The larger a is, the narrower your curve will be (i.e. the 2 downturned sides will be closer to each other).
There are a lot more but I'll stop here, seeing you're probably just required to know the basics of quadratic equations. :)