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0. Fundamental Concepts of Algebra(0)

Algebraic Expressions
(0)

Exponents
(0)

Polynomials Intro
(0)

Multiplying Polynomials
(0)

Factoring Polynomials
(0)

Radical Expressions
(0)

Simplifying Radical Expressions
(0)

Rationalize Denominator
(0)

Rational Exponents
(0)

Pythagorean Theorem & Basics of Triangles
(0)

1. Equations and Inequalities(0)

Linear Equations
(0)

Rational Equations
(0)

The Imaginary Unit
(0)

Powers of i
(0)

Complex Numbers
(0)

Intro to Quadratic Equations
(0)

The Square Root Property
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Completing the Square
(0)

The Quadratic Formula
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Choosing a Method to Solve Quadratics
(0)

Linear Inequalities
(0)

2. Graphs(0)

Graphs and Coordinates
(0)

Two-Variable Equations
(0)

Lines
(0)

3. Functions & Graphs(0)

Intro to Functions & Their Graphs
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Common Functions
(0)

Transformations
(0)

Function Operations
(0)

Function Composition
(0)

4. Polynomial Functions(0)

Quadratic Functions
(0)

Understanding Polynomial Functions
(0)

Graphing Polynomial Functions
(0)

5. Rational Functions(0)

Introduction to Rational Functions
(0)

Asymptotes
(0)

Graphing Rational Functions
(0)

6. Exponential and Logarithmic Functions(0)

Introduction to Exponential Functions
(0)

Graphing Exponential Functions
(0)

The Number e
(0)

Introduction to Logarithms
(0)

Graphing Logarithmic Functions
(0)

Properties of Logarithms
(0)

Solving Exponential and Logarithmic Equations
(0)

7. Measuring Angles(0)

Angles in Standard Position
(0)

Coterminal Angles
(0)

Complementary and Supplementary Angles
(0)

Radians
(0)

8. Trigonometric Functions on Right Triangles(0)

Trigonometric Functions on Right Triangles
(0)

Special Right Triangles
(0)

Cofunctions of Complementary Angles
(0)

Solving Right Triangles
(0)

9. Unit Circle(0)

Defining the Unit Circle
(0)

Trigonometric Functions on the Unit Circle
(0)

Common Values of Sine, Cosine, & Tangent
(0)

Reference Angles
(0)

Reciprocal Trigonometric Functions on the Unit Circle
(0)

10. Graphing Trigonometric Functions(0)

Graphs of the Sine and Cosine Functions
(0)

Phase Shifts
(0)

Graphs of Secant and Cosecant Functions
(0)

Graphs of Tangent and Cotangent Functions
(0)

11. Inverse Trigonometric Functions and Basic Trig Equations(0)

Inverse Sine, Cosine, & Tangent
(0)

Evaluate Composite Trig Functions
(0)

Linear Trigonometric Equations
(0)

12. Trigonometric Identities (0)

Introduction to Trigonometric Identities
(0)

Sum and Difference Identities
(0)

Double Angle Identities
(0)

Solving Trigonometric Equations Using Identities
(0)

13. Non-Right Triangles(0)

Law of Sines
(0)

Law of Cosines
(0)

Area of SAS & ASA Triangles
(0)

14. Vectors(0)

Geometric Vectors
(0)

Vectors in Component Form
(0)

Direction of a Vector
(0)

Unit Vectors and i & j Notation
(0)

Dot Product
(0)

Cross Product
(0)

15. Polar Equations(0)

Polar Coordinate System
(0)

Convert Points Between Polar and Rectangular Coordinates
(0)

Convert Equations Between Polar and Rectangular Forms
(0)

Graphing Other Common Polar Equations
(0)

16. Parametric Equations(0)

Graphing Parametric Equations
(0)

Eliminate the Parameter
(0)

Writing Parametric Equations
(0)

17. Graphing Complex Numbers(0)

Graphing Complex Numbers
(0)

Polar Form of Complex Numbers
(0)

Products and Quotients of Complex Numbers
(0)

Powers of Complex Numbers (DeMoivre's Theorem)
(0)

18. Systems of Equations and Matrices(0)

Two Variable Systems of Linear Equations
(0)

Introduction to Matrices
(0)

Determinants and Cramer's Rule
(0)

Graphing Systems of Inequalities
(0)

19. Conic Sections(0)

Introduction to Conic Sections
(0)

Circles
(0)

Ellipses: Standard Form
(0)

Parabolas
(0)

Hyperbolas at the Origin
(0)

Hyperbolas NOT at the Origin
(0)

20. Sequences, Series & Induction(0)

Sequences
(0)

Arithmetic Sequences
(0)

Geometric Sequences
(0)

21. Combinatorics and Probability(0)

Factorials
(0)

Combinatorics
(0)

Probability
(0)

22. Limits & Continuity(0)

Introduction to Limits
(0)

Finding Limits Algebraically
(0)

Continuity
(0)

23. Intro to Derivatives & Area Under the Curve(0)

Tangent Lines & Derivatives
(0)

Limits at Infinity
(0)

Limits of Sequences
(0)

Area Under a Curve
(0)

19. Conic Sections

Ellipses: Standard Form

19. Conic Sections

Ellipses: Standard Form: Video e Problemi di Pratica

Videolezioni Pratica Foglio di lavoro

16 problemi

Problema 1Scelta multipla

Work out the standard form of the ellipse equation, given the following conditions.

Vertices: (0, - 9) and (0, 9)
Passes through the point: (12, 3)

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Problema 2Scelta multipla

Find the equation of the ellipse with the following properties. Express your answer in standard form.

Major axis vertical length = 14; length of minor axis = 6; center: (-1, 2)

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Problema 3Scelta multipla

Graph the following ellipse and determine its foci: y² = 1 - 16x²

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Problema 4Scelta multipla

The graph of the ellipse is given below. Find its standard equation and the coordinates of the foci.

Graph of an ellipse with labeled foci and axes, illustrating standard form.

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Problema 5Scelta multipla

Graph the given ellipse and indicate its foci.

Ellipse equation in standard form: (x-3)²/36 + (y-4)²/25 = 1.

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Problema 6Scelta multipla

The blue ellipse shown in the figure is defined by x²/36 + y²/81 = 1. Determine the equation of the two circles.

Graph showing a blue ellipse and two concentric circles in green and brown.

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Problema 7Scelta multipla

Which of the following best describes an ellipse?

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Problema 8Scelta multipla

What distinguishes an ellipse from a circle?

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Problema 9Scelta multipla

Given a horizontal ellipse with a semi-major axis of 5 and a semi-minor axis of 3, what is its equation?

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Problema 10Scelta multipla

Given a vertical ellipse with a semi-major axis of 6 and a semi-minor axis of 4, what is its equation?

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Problema 11Scelta multipla

For an ellipse with a semi-major axis of 10 and a semi-minor axis of 6, what is the distance to the foci from the center?

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Problema 12Scelta multipla

Given the equation (x-1)^2/49 + (y+3)^2/25 = 1, which axis is the major axis?

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Problema 13Scelta multipla

What is the geometric definition of an ellipse?

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Problema 14Scelta multipla

How does the presence of semi-major and semi-minor axes affect the shape of an ellipse compared to a circle?

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Problema 15Scelta multipla

What is the equation of a horizontal ellipse with a semi-major axis of 8 and a semi-minor axis of 5?

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Problema 16Scelta multipla

What is the equation of a vertical ellipse with a semi-major axis of 9 and a semi-minor axis of 4?

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Circles Problemi di pratica Parabolas Problemi di pratica

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Ellipses: Standard Form: Video e Problemi di Pratica

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