Problem 88 - Introductory Algebra for College Students

Question

What is a quadratic equation?

Step-by-Step Solution

Answer

A quadratic equation is a second-order polynomial equation in a single variable \(x\), with a nonzero coefficient for \(x^2\). It is typically represented in this standard form: \(ax^2 + bx + c = 0\).

Step 1: Definition of Quadratic Equation

A quadratic equation is a second-order polynomial equation that can be expressed in the standard form \(ax^2 + bx + c = 0\), where \(a\), \(b\), and \(c\) are coefficients, \(a ≠ 0\), and \(x\) represents an unknown variable.

Step 2: Identifying the Quadratic Equation

The equation should hold the form stated above and it's recognized by the highest exponent being 2. That's why it's a 'quadratic', which comes from 'quad' meaning square – as in \(x^2\).

Step 3: Understanding Coefficients

In the equation, three numbers define its structure - \(a\), \(b\), and \(c\). These are coefficients that, when varied, will change the parabolic shape of the graph that represents the quadratic equation.