Analyzing Quadratic Functions and Limits

Analyzing Quadratic Functions and Limits

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Practice Problem

Hard

Created by

Thomas White

FREE Resource

The video tutorial explains how to evaluate the limit of a function as x approaches 1, specifically for the function (x^3 + 4x^2 - 5x) / (x - 1). Initially, substitution is used, but it results in an indeterminate form (0/0), indicating a discontinuity. The tutorial then demonstrates how to factorize the numerator to eliminate the common factor (x - 1), allowing the limit to be calculated as 6. The video also covers the graphical representation of the function, highlighting the hole at x = 1 and the overall parabolic shape.

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15 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the initial problem presented in the video?

Evaluating the limit of a function as x approaches 1

Integrating a polynomial function

Finding the derivative of a function

Solving a quadratic equation

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What result do we get when substituting x = 1 directly into the function?

A negative number

An indeterminate form 0/0

An infinite value

A finite number

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does the indeterminate form 0/0 indicate about the function at x = 1?

The function is continuous

The function has a hole or discontinuity

The function is undefined everywhere

The function has a vertical asymptote

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the common factor in the numerator and denominator that causes the indeterminate form?

X + 1

X - 1

X + 5

X - 5

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the product of the two numbers used in factorizing the quadratic expression?

-4

4

5

-5

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the sum of the two numbers used in factorizing the quadratic expression?

4

-5

-4

5

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

After canceling the common factor, what expression do we use to find the limit?

x^2 + 4x - 5

x(x + 5)

x^3 + 4x^2 - 5x

x - 1

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