Chapter 7
Quadratic Equations
A square patio covering nine square feet has sides of three feet, and you can work that out in your head. Now ask for a patio of twenty square feet, or a rectangular one that must be three feet longer than it is wide. In both, the unknown length gets multiplied by itself, and undoing the equation one step at a time no longer works. Equations where a letter multiplies itself are called quadratic, and a single one of them can hold more answers than you would expect.
What You'll Explore
4 lessons.
- Introduction to Quadratics
What has to be true of a number if squaring it gives one hundred? The obvious answer may not be the only one. This lesson pins down what makes an equation quadratic, what it means for a value to solve one, and how many solutions a single equation can have.
- Factoring Quadratics
Expanding two simple factors into a quadratic is routine by now. Running that backwards, starting from the quadratic and recovering the factors it came from, is a genuine puzzle. This lesson builds a dependable way to search for them, and shows what having the factors lets you do.
- Factoring Harder Quadratics
Put a number in front of the squared term and the search from the previous lesson stops working straight away. Where does that number come from, and what does it change about the two factors you are hunting for? This lesson takes on quadratics of that shape, including solutions that are no longer whole numbers.
- Sums and Products of Roots
Add the two solutions of a quadratic you have just factored, then multiply them, and compare both results with the numbers in the original equation. Something is going on there. This lesson follows that pattern, and finds that it runs in reverse as well, letting you start from the solutions you want and build the equation around them.