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!! :)

Post something in particular. It is a broad subject.

I don't understand the fromula part of the problem.

You mean ax^{2}+bx+c?

A quadratic equation describes a parabola.

Like this http://www.mathwarehouse.com/quadratic/images/quadratic-formula-example.gif

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? :)

Yes it was! And thank you so much! That cleared everything up for me!

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. :)