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 ?

A quadratic equation describes a parabola.

Like this

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:

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

a=2, b=5, c=-6

Plug them into the quad formula:



Now do the 'minus' case:



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

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'.

See? That is the part inside the radical. We can use that to find out what sort of solutions it has.

For your , the discriminant is

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. :)