# Quadratic Formula and Functions Exercises

#### Imaginary and Complex Numbers

It's finally come to this, has it? We've run out of actual numbers to throw at you, so now we're just going to make some numbers up? Not really. Imaginary numbers, despite the name, are totally l...

#### Completing the Square

Sample Problem Solve the quadratic equation x2 + 2x + 5 = 0. Hmm, now this is tricky. This equation is—most definitely—not factorable. It would be really convenient if it were fact...

#### Quadratic Formula

Completing the square always works when solving a quadratic equation, but it's almost always a pain in the butt to actually do. We want a method that's faster and easier to use while being just as...

#### How Many Roots?

When you solve for the roots of a quadratic equation, there are several possible outcomes. You can have two real number solutions. If you set x equal to either solution, the result with be zer...

#### Vertex Form Parabolas

The difficulty of graphing a quadratic function varies depending on the form you find it in. We'll start things off relatively easily. f(x) = a(x – h)2 + k No, we're not lying to you;...

#### Quadratic Form Parabolas

The vertex form for parabolas is convenient for graphing, but oftentimes you'll be given the equation in the usual quadratic form instead. f(x) = ax2 + bx + c Can we deduce a way to fin...

#### Quadratic-Like Equations

Sometimes you'll meet an equation that you think you don't know, and you'll start up a conversation. After a few minutes of talking, though, it finally hits you—this is just like a quadratic eq...

#### Quadratic Inequalities

Remember back when we looked at linear inequalities? At one point, we said, "We promise we'll try to make your brain hurt more later." We always keep our promises, so grab an ice pack and strap...