y = x²: Challenge & Extension
Mathematics
Grade 8
12 questions
~24 mins
1 views0 downloads
About This Worksheet
This worksheet explores the quadratic function y = x², focusing on plotting, analyzing, and applying parabolas. Designed for challenge and extension, it enhances understanding of quadratic graphs and their properties.
Worksheet Preview
Full preview • 12 questions
y = x²: Challenge & Extension
Subject: MathematicsGrade: Grade 8
Name:
Date:
TeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizz
Untitled Worksheet
Grade Grade 8
A
Fluency & Practice
Plot the graph of y = x² for the given x-values and find their corresponding y-values. Show your work on the grid.
1.
Calculate y when x = -3, -2, -1, 0, 1, 2, 3 for y = x².
[4 marks]2.
Plot the points for x = -2, -1, 0, 1, 2 on the grid and connect them smoothly to form the parabola.
[3 marks]3.
Identify the vertex of the parabola y = x² and state its coordinates.
[2 marks]B
Problem Solving & Reasoning
Use your understanding of y = x² to solve these multi-step problems. Show detailed working.
1.
If the parabola y = x² is shifted 3 units to the right and 2 units up, what is the equation of the new parabola? Plot its vertex.
[4 marks]2.
Determine the x-values where y = 16 on the graph of y = x². Show your calculations.
[3 marks]3.
Explain why the parabola y = x² is symmetric. Support your answer with reference to its vertex and points.
[4 marks]C
Real-world Applications
Solve these word problems by relating them to the graph of y=x². Show your reasoning clearly.
1.
A ball is thrown upward so that its height in meters is modeled by y = -x² + 4x, where x is time in seconds. When does the ball reach its maximum height? What is this maximum height?
[4 marks]2.
A rectangular garden's length is modeled by y = x² meters, where x is a variable length. Find the length when the area reaches 16 square meters, given that width is x meters.
[3 marks]D
Challenge & Extension
Attempt these advanced problems that extend your understanding of y = x² and parabolas. Provide detailed solutions.
1.
Derive the vertex form of y = x² and explain how transformations affect the graph's vertex. Illustrate with an example.
[4 marks]2.
If the parabola y = (x - 1)² + 5 is reflected across the x-axis, what is its new equation? Plot the new vertex.
[3 marks]E
Mixed Review & Error Analysis
Review these questions carefully. For the common mistake question, identify and correct the error in the student’s solution.
1.
A student plots y = x² but forgets to plot the point (0,0). How does this mistake affect the graph? Correct the graph and explain.
[3 marks]2.
Identify the mistake: A student claims y = x² is a linear function. Explain why this is incorrect.
[3 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet