Solving a Second-Degree Polynomial

Graph It Factor it Quadratic Equation You Can You get the two solutions, but

it can be hard to tell where they are

Sometimes you get a nasty decimal, like .304682...

This is way easy, but it only works sometimes. This is where you can make your equation look something like (x-p)(x-q)=0 This is the weird-looking thing that says First, factor out an a But just from part of it We can add this because it's really just zero! (Any number minus itself is zero) We have to exclude this part. All we really did was multiply the "a" back through, then factor it out again. Here's the proof for it. Remember this? All that becomes this! This gets subtracted to the other side. Multiply "c" by "4a" And divide by "4a" If you multiply a number by something, then divide by the same thing, it doesn't do anything to the number.

Since the denominator (the bottom of the fraction) is the same... We can combine them! Now we divide both sides by Square root both sides The absolute value signs | and | are there because a square root is always positive Square root the top and the bottom. Since the part inside | | can be either positive or negative with the same result... We get this "plus or minus" sign Now we can subtract this part to isolate x!

Since the denomitator is the same, we can combine the two fractions.

Hey, we're done! Dividing by "a" is the same thing as putting another "a" in the denominator. Since we have two "a"s in the denominator, it's "a squared." They look like this.

By "solve," we mean "find x." This gives us the "roots" or solutions x=p and x=q There is a way that always works... Ever wonder where this thing comes from? This is called the distributive property. It works on groups of terms, too. Pretend this part is one thing.

Distribute it through. Then distribute F and G through. We can do this backwards.

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# Quadratic Formula

Ever wondered where the quadratic formula came from? Here's your chance to find out for yourself.

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