Conic Sections and Completing the Square

Conic Sections and Completing the Square

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Practice Problem

Hard

Created by

Thomas White

FREE Resource

The video tutorial by Mark Heros on MathGuide.com explains how to transform a conic section equation from general form to standard form. It begins by identifying the type of conic section, which is determined to be a hyperbola. The tutorial then walks through the process of grouping terms, factoring, completing the square, and balancing the equation to achieve the standard form of a hyperbola. The video concludes with a discussion on graphing the hyperbola and determining its properties.

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10 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the general form of a conic section?

An equation that looks like a polynomial

An equation with parentheses

An equation with no coefficients

An equation with only linear terms

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which conic section has equal coefficients for squared terms?

Parabola

Ellipse

Circle

Hyperbola

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What indicates that a conic section is a hyperbola?

Coefficients of squared terms with the same sign

Coefficients of squared terms with different signs

Equal coefficients for squared terms

One squared term

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in transforming the equation into standard form?

Divide all terms by the same number

Multiply all terms by a constant

Lump all x and y terms together

Add a constant to both sides

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why do we factor out the coefficient of the squared term?

To make the coefficient of the squared term equal to one

To eliminate the squared term

To simplify the equation

To add a constant to both sides

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the purpose of completing the square?

To eliminate the squared term

To create a perfect square trinomial

To add a constant to both sides

To simplify the equation

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How do you balance the equation after completing the square?

Divide both sides by the same number

Multiply both sides by the same number

Subtract the same constant from both sides

Add the same constant to both sides

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