Understanding Quadratic Functions and Their Applications

Understanding Quadratic Functions and Their Applications

Assessment

Interactive Video

Created by

Aiden Montgomery

Mathematics, Business

9th - 12th Grade

Hard

This lesson teaches how to find maximum and minimum values of real-world functions by completing the square. It explains the vertex form of quadratic functions and how to determine if a vertex is a maximum or minimum. The lesson includes examples of maximizing revenue and minimizing cost by rewriting functions in vertex form. It concludes with a review of key concepts.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the purpose of using the vertex form of a quadratic function?

To find the slope of the function

To identify the vertex and determine if it's a maximum or minimum

To determine the y-intercept

To calculate the area under the curve

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

When the coefficient 'a' in a quadratic function is negative, what does the vertex represent?

A zero of the function

A maximum point

A minimum point

A point of inflection

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in completing the square for a quadratic function?

Add a constant to both sides

Factor out the leading coefficient

Multiply the entire equation by 2

Divide the entire equation by the leading coefficient

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How do you confirm that a production level yields maximum revenue?

By checking if the revenue is higher than the previous week

By ensuring the production cost is minimized

By comparing revenues at production levels just below and above the vertex

By calculating the derivative of the revenue function

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the vertex of the revenue function in the example provided?

(500, 500,000)

(100, 2200)

(0, 0)

(250, 250,000)

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the context of minimizing costs, what does a positive 'a' value indicate?

The function has no vertex

The function is linear

The vertex is a minimum

The vertex is a maximum

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the minimum cost of production in the widget example?

$20,000

$2,200

$500,000

$10,000

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