About This Chapter
Quadratic Polynomials & Parabolas - Chapter Summary
Our helpful chapter on quadratic polynomials and parabolas explains quadratic functions, equations, formulas and graphs. You'll review the process involved in solving and graphing quadratic inequalities and the explanation of what a discriminant is. Our lessons also cover the identity of two quadratic expressions and the focus and directrix of a parabola. This chapter is designed to help you:
- Differentiate between indefinite and definite quadratic functions
- Use the focus and directrix to find the equation of a parabola
- Understand parametric equations in applied contexts
The video and text lessons in this chapter were created by professional instructors to make sure your study experience is thorough and enjoyable. After reviewing the lessons, take the multiple-choice quizzes to test yourself on what you've learned. Or take the quizzes before working through the lessons to see how you'd do on an upcoming exam. Feel free to reach out to an instructor for assistance if you need it.
1. Quadratic Functions: Examples & Formula
Learn what sets quadratic functions apart from all other functions. Learn how you can spot a quadratic just by looking at its graph. Also learn the two formulas that will help you when working with them.
2. Quadratics: Equations & Graphs
We will look at quadratic equations: what they are, some forms in which we might find them, how we can put them into standard form, and how their graphs look, including some features of the graphs.
3. Graphing & Solving Quadratic Inequalities: Examples & Process
When you finish watching this video lesson, you will be able to graph and solve your own quadratic inequality. Learn what steps you need to take and what to watch for.
4. Discriminant: Definition & Explanation
The discriminant helps you to solve quadratic equations. In this lesson, you will learn how to identify the discriminant and how to use it to help you find the number of solutions in a quadratic equation.
5. Definite and Indefinite Quadratic Functions
Quadratic functions can be described as definite or indefinite based on where they lie on the x-y plane. In this lesson, we will investigate what makes a quadratic definite or indefinite.
6. Identity of Two Quadratic Expressions
In this lesson, we will discuss the standard form of a quadratic expression. We will also use the standard forms of quadratic expressions to determine whether or not two expressions are identical.
7. The Focus and Directrix of a Parabola
In this lesson, we will review what a parabola is, then we will look at the formal definition of a parabola, introducing the focus and directrix of a parabola. We will look at some examples to help solidify our understanding of these concepts.
8. Finding the Equation of a Parabola from the Focus and Directrix
A parabola is the familiar shape seen in many physical applications, like the path taken by a ball thrown upwards. This lesson explores equations for the parabola and shows how they may be obtained from two quantities: the focus and the directrix.
9. Parametric Equations in Applied Contexts
Watch this video lesson to learn how you can use parametric equations to help you solve real world problems such as the path of a moving object. Learn how to form parametric equations to model the real world.
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Other chapters within the HSC Mathematics: Exam Prep & Syllabus course
- Mathematical Proofs & Reasoning
- Basic Arithmetic & Algebra
- Factorization of Binomials & Trinomials
- Types of Equations & Inequalities
- Plane Geometry
- Circle Plane Geometry
- Probability & Randomization
- Arithmetic & Geometric Series
- Trigonometric Ratios
- Geometrical Representations of Functions
- Linear Functions & Lines
- Derivatives of Functions
- Geometrical Applications of Differentiation
- Logarithmic & Exponential Functions
- Calculating Trigonometric Functions
- Understanding Inverse Functions
- Factoring & Graphing Polynomials
- Roots & Coefficients of Polynomials
- Binomial Theorem & Probability
- Graphing & Solving Functions
- Solving & Graphing Complex Numbers
- Geometric Representations of Complex Numbers
- Square Roots, Powers & Roots of Complex Numbers
- Conic Sections Basics
- The Ellipse in Algebra
- The Hyperbola
- The Rectangular Hyperbola
- Calculus Applications: Rate of Change
- Calculus Applications: Velocity & Acceleration
- Calculus Applications: Projectile & Harmonic Motion
- Calculus Applications: Resisted Motion
- Calculus Applications: Circular Motion
- HSC Mathematics Flashcards