This week, we learned how to learn if a quadratic equation had one solution, two solutions, or no solutions using the discriminate. What is the discriminate, you may ask? Look at your quadratic equation, see the expression inside the square root? That’s your discriminant.

If you don’t remember, represents the first term’s coefficient, %latex b$ represents the second/middle term’s coefficient, and %latex c$ represents the third/last term’s coefficient.

Say your quadratic equation is , then the discriminate would be…

The discriminant is

The discriminant can tell us whether the answer has two solutions, one solution, or no solutions. If the discriminant is positive, then there are two solutions to your quadratic equation. If the discriminant equals zero, there will be one solution. However, if the discriminant is negative, then your quadratic equation has no solutions.

What’s a solution? Glad you asked, if you attempt to graph a quadratic equation, your line isn’t a line! It’s this little bendy thing, which is called a parabola. For a quadratic equation to have a solution, a part of it has to be touching the x-axis. So, if the para

bola touches two points on the x-axis, then it has two solutions. However, if the apex of the parabola touches the x-axis, then that means the equation only has one solution. And if the parabola doesn’t touch the x-axis? No solutions.