y = ax² + bx + c: Real-world Applications in Medicine & Health
Mathematics
Grade 6
13 questions
~26 mins
1 views0 downloads
About This Worksheet
A worksheet exploring the application of quadratic functions y = ax² + bx + c in medicine and health contexts, including plotting, calculations, and problem-solving.
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y = ax² + bx + c: Real-world Applications in Medicine & Health
Subject: MathematicsGrade: Grade 6
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Untitled Worksheet
Grade Grade 6
A
Fluency & Practice
Answer the following questions by calculating or plotting on the grid. Show your working clearly.
1.
Plot the graph of y = 2x² + 3 on the grid. Identify the vertex of the parabola.
[3 marks]2.
Calculate y when x = 4 for y = -x² + 2x + 5.
[2 marks]3.
Plot y = -x² + 4x + 1 and find the y-value when x = -1.
[3 marks]B
Problem Solving & Reasoning
Work through these multi-step problems, explaining your reasoning clearly.
1.
A medicine's effectiveness over time is modeled by y = -0.5t² + 4t + 10, where t is hours after administration. How long does it take for the effectiveness to reach its maximum? What is the maximum effectiveness?
[4 marks]2.
The height of a balloon over time is modeled by y = -2t² + 8t + 2. When does the balloon hit the ground (y=0)?
[3 marks]C
Real-world Applications
Use the quadratic formula or plotting to solve these health-related problems.
1.
A drug's effect follows the quadratic y = -0.3x² + 3x + 5, where y is the effectiveness level. At what time is the effectiveness at its peak? What is the peak effectiveness?
[4 marks]2.
A health study shows the relation y = -x² + 6x + 2 between exercise duration (x in hours) and energy level (y). How long should a person exercise to maximize their energy? What is that maximum energy level?
[4 marks]D
Challenge & Extension
Attempt these more advanced problems involving quadratic functions in health contexts.
1.
A medication's efficacy over time is modeled by y = -0.4t² + 5t + 7. Find the time when efficacy drops to 10. Show your working.
[4 marks]2.
Construct a parabola on the grid representing y = -x² + 2x + 4 that models a health scenario where the maximum effectiveness is critical. Describe the key features of the parabola.
[3 marks]E
Mixed Review
Answer these questions to review your understanding of y = ax² + bx + c.
1.
Identify the coefficients a, b, c in y = -3x² + 6x + 1 and describe what the parabola looks like.
[3 marks]2.
Plot y = 0.5x² - 2 on the grid. Find the roots of the equation.
[3 marks]F
Error Analysis
Identify the mistake in each problem and correct it.
1.
A student plots y = x² + 4x + 3 but forgets to shift the parabola vertically. What is the mistake, and how should they correctly plot the parabola?
[3 marks]2.
A calculation shows y = -2x² + 4x + 1 at x=2 gives y= -3, but the student reports y=3. Identify and fix the error.
[2 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)
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet