Kenny

Q: What can you tell about the graph of a quadratic function based on the roots you get from solving the quadratic formula for that equation?

 A: The roots that you get from solving the quadratic formula for a givin equation will show you the x-intercepts for the graph. If the result comes up with one root, it means your x-int.'s are the same, in other words there is only one. If you get no roots, your graph has no x-int.'s and if you get two roots, you have two x-int.'s. These are shown below, green representing two x-int.'s, purple representing no x-int.'s and yellow representing one x-int.

http://www.enchantedlearning.com/math/algebra/quadratic/gifs/parabolas.GIF

You can tell when you will get each of these situations by using the quadratic formula . In the formula, the number in the square root, represented as , is the discriminant. If the discriminant is positive, you will get two roots, if it is negative, you will get two unreal numbers, and if it is zero, you will get one root. You find this by plugging the numbers from your equation into the formula, and solve for it. When solving you will come across the  sign, this is how you get your two different answers from the one equation. You first solve for the +, then solve for the -. The two numbers you get after solving them are your roots.

Ex:

This means your equation will be:

Using the equation you know the discriminant is  and when solving that you get 36.

Knowing the discriminant is a positive number, you will have two roots when you solve the equation.

After solving you prove that you do get two roots for the equation.