Critical Values: Real-world Applications

Mathematics
Grade 8
12 questions
~24 mins
1 views0 downloads

About This Worksheet

This worksheet explores the concept of critical values in quadratic inequalities through real-world shopping and money scenarios. Students will identify and analyze critical points to make decisions based on quadratic models.

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Full preview • 12 questions

Critical Values: Real-world Applications

Subject: MathematicsGrade: Grade 8
Name:
Date:
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Untitled Worksheet

Grade Grade 8
A

Fluency & Practice

Answer all questions. Show your working in the grid spaces provided.
1.
Find the critical value of the quadratic function y = x^2 - 6x + 8.
[2 marks]
2.
Determine the critical points of the quadratic y = -2x^2 + 4x + 5.
[2 marks]
3.
Calculate the x-coordinate of the vertex for y = 3x^2 - 12x + 7.
[2 marks]
B

Problem Solving & Reasoning

Answer all questions with detailed explanations.
1.
A shop offers a discount on a jacket such that the price after discount is modeled by y = -x^2 + 4x + 50, where x is the discount percentage. Find the critical value to determine the maximum discounted price and interpret its meaning.
[4 marks]
2.
A student's savings after shopping is modeled by S = -2t^2 + 8t + 20, where t is the number of weeks. Find the critical value of t and explain its significance.
[4 marks]
C

Real-world Applications

Answer all questions based on the given shopping scenarios.
1.
A store sells a jacket where the profit in dollars is modeled by P = -x^2 + 5x - 3, with x representing the number of jackets sold. Find the critical value of x and interpret its significance for maximum profit.
[3 marks]
2.
A customer wants to maximize their savings by choosing how much to spend, modeled by S = -x^2 + 6x + 10. Find the critical value of x and explain how it helps in decision making.
[3 marks]
D

Challenge & Extension

Attempt these advanced problems to deepen your understanding.
1.
The profit function for a sale is given by P(x) = -x^2 + 4x + 100. If a discount is applied such that the price decreases, find the critical value and analyze how it influences the maximum profit.
[4 marks]
2.
A quadratic model for total revenue R(x) = -3x^2 + 12x + 75 predicts revenue based on units sold x. Determine the critical value and interpret its importance.
[4 marks]
E

Mixed Review

Answer a variety of question types to review your understanding.
1.
Identify the critical value of the quadratic y = 2x^2 - 8x + 3.
[2 marks]
2.
Construct a parabola on the grid representing y = -x^2 + 4x + 1 and find its critical point.
[3 marks]
F

Error Analysis

Review the following mistake and identify the correction needed.
1.
A student calculates the critical value of y = x^2 - 4x + 7 as x=4. Is this correct? If not, find the correct critical value and explain the mistake.
[3 marks]

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Details

Created
1/1/2026
Updated
1/1/2026
Type
worksheet