What does “solving” mean?

To solve a quadratic or polynomial means to find the value(s) of $x$ that make the expression equal zero.

Example:

x^2 – 4 = 0

We are looking for values of $x$ that make this true.

What is a quadratic?

A quadratic is a polynomial where the highest power of $x$ is 2.

General form:

ax^2 + bx + c = 0

Quadratics can have:

• Two solutions

• One solution

• No real solutions

What do solutions represent?

Solutions can be:

• x-intercepts of a graph

• Zeros of the function

• Points where the graph crosses the x-axis

All mean the same thing.

Why are there different solving methods?

Because:

• Some quadratics factor easily

• Some do not

• Some are easier to solve visually

• Some require a formula