Algebra 64 - Quadratic Functions and Polynomials

TL;DR

This lecture introduces quadratic functions, which are defined by the expression ax^2 + bx + c, and explains their basic properties.

Transcript

Hello. I'm Professor Von Schmohawk and welcome to Why U. In this lecture, we will introduce "quadratic functions". A quadratic function of x is any function which can be defined by the expression a x-squared + bx + c where a, b, and c are constants which determine the shape and position of the function's graph. We will refer to a quadratic functi... Read More

Key Insights

• 😃 Quadratic functions are defined by the expression ax^2 + bx + c, where a, b, and c are constants.
• 📈 The graph of a quadratic function is a parabola, with a vertex and an axis of symmetry.
• ❓ The value of the constant a determines the direction and width of the parabola.
• ☺️ Quadratic functions are a specific type of polynomial, with the highest power of x being 2.
• 🍉 Polynomial expressions can have any finite number of terms, including quadratic terms.
• 💌 The coefficients in polynomials can be represented using letters with numerical subscripts.
• ❓ Quadratic functions can be trinomials, binomials, or monomials.

Questions & Answers

Q: What is a quadratic function and how is it defined?

A quadratic function is defined by the expression ax^2 + bx + c, where a, b, and c are constants. The x^2 term is necessary for a function to be quadratic.

Q: What does the graph of a quadratic function look like?

The graph of a quadratic function is a parabola. The shape of the parabola, its vertex, and axis of symmetry depend on the values of a, b, and c.

Q: What is the difference between a quadratic function and a linear function?

A quadratic function includes an x^2 term, while a linear function only has terms up to x^1. This results in different graph shapes and behaviors.

Q: How are polynomials related to quadratic functions?

A quadratic function is a second-degree polynomial since its highest power of x is 2. Polynomials can have any finite number of terms, including quadratic terms.

Summary & Key Takeaways

• Quadratic functions are defined by the expression ax^2 + bx + c, where a, b, and c are constants that determine the shape and position of the function's graph.

• The graph of a quadratic function is a parabola, with a vertex that serves as the turning point and an axis of symmetry.

• The value of the constant a determines whether the parabola opens up or down and its width.