Problem 51 - College Algebra

Question

What is a quadratic function?

Step-by-Step Solution

Answer

A quadratic function is a type of polynomial with the form \(y = ax^2 + bx + c\), where \(a\), \(b\), and \(c\) are constants and \(a \neq 0\). Its graph is a parabola.

Step 1: Definition

A quadratic function is a type of polynomial function that has the general form \(y = ax^2 + bx + c\), where \(a\), \(b\), and \(c\) are constants, and \(a\) is not equal to zero.

Step 2: Features of a Quadratic Function

The graph of a quadratic function is a parabola which opens upward if \(a > 0\), and downward if \(a < 0\). The 'vertex' is the highest or lowest point of the parabola. If the parabola opens upwards, the vertex is the minimum point and vice versa. The line of symmetry of the parabola is the vertical line through the vertex.

Step 3: Examples of Quadratic Functions

Examples: \(y = 2x^2 + 3x - 4\), \(y = -x^2 + 5x + 6\), etc. These are quadratic functions because they follow the form \(y = ax^2 + bx + c\).