B. An Introduction to Quadratic Equations

A quadratic equation is a single-variable polynomial equation of degree two. This means that the equation will include a squared variable just like a quadratic function. The standard form of a quadratic equation is

Solving a quadratic equation means determining the value or values of the variable that make the equation true. These variable values are called the solutions or roots of the equation. Because of your work in Lesson 2.2 on finding the x-intercepts of the graph of a quadratic function given in factored form, you are already well-equipped to solve quadratic equations.

Recall that to find the x-intercepts of the graph of a quadratic function or the zeros of the quadratic function, you found the x-values that made the function equal to zero. By substituting 0 for y or f(x), you created (and then solved) a quadratic equation. The x-intercepts of the graph of a quadratic function and the zeros of a quadratic function are actually the solutions to the corresponding quadratic equation.

The function has −2 and 3 as zeros. The graph of the function has x-intercepts at −2 and 3. This means −2 and 3 are the solutions to the quadratic equation .

Recall that a quadratic function can have 0, 1, or 2 Real Number zeros and the graph of a quadratic function can have 0, 1, or 2 x-intercepts. As such, a quadratic equation can have 0, 1, or 2 Real solutions.