Quadratic Polynomial

A quadratic polynomial is a polynomial of degree 2. It is an expression of the form:

ax² + bx + c

• a: the coefficient of the quadratic term (x²)
• b: the coefficient of the linear term (x)
• c: the constant term

Standard Form of Quadratic Polynomial

The standard form of a quadratic polynomial is given as:

ax² + bx + c = 0

Where a, b, and c are constants, and a ≠ 0.

Graph of Quadratic Polynomial

The graph of a quadratic polynomial is a parabola. The direction of the parabola (upwards or downwards) and the vertex can be determined from the sign of the coefficient 'a'.

Study Guide

Here are some key points to remember about quadratic polynomials:

1. Identify the coefficients a, b, and c in the quadratic polynomial expression.
2. Understand the standard form of a quadratic polynomial and its relation to the graph of the function.
3. Learn how to factorize or solve the quadratic equation using different methods such as factoring, completing the square, or using the quadratic formula.
4. Practice graphing quadratic functions and identifying the vertex, axis of symmetry, and intercepts.

Understanding quadratic polynomials is essential in algebra and mathematics, as they have wide applications in real-world problem-solving and various fields of science.