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Graph-Equation Matching Exercise
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Graph-Equation Matching Exercise
Match each curve description to one equation. Then answer the questions about function features and applications. Show working where helpful.
Match curves and equations
Match each description with the equation that produces it. Each equation is used once.
1.Match each curve description to an equation: A. A straight line with y-intercept 2 and gradient 3; B. An upward-opening parabola with vertex (0, −3); C. An increasing exponential curve passing through (0, 1); D. A cubic curve through the origin with a positive leading coefficient; E. A horizontal line at y = 4; F. A downward-opening parabola with vertex (1, 6).
- A. Line with y-intercept 2 and gradient 3
- B. Upward parabola with vertex (0, −3)
- C. Increasing exponential through (0, 1)
- D. Cubic through the origin, positive leading coefficient
- E. Horizontal line at y = 4
- F. Downward parabola with vertex (1, 6)
- y = 3x + 2
- y = −(x − 1)² + 6
- y = 4
- y = x² − 3
- y = 3ˣ
- y = x³
Function features
Use function properties and algebra to answer each question.
2.For f(x) = −2x² + 8x + 1, state the y-intercept, whether the parabola opens up or down, the x-coordinate of its vertex, and its maximum or minimum value.
3.A model for a town’s population is P(t) = 800(1.04)ᵗ, where t is the number of years after the model begins. Find the initial population, the annual percentage growth rate, and the predicted population after 8 years, rounded to the nearest whole person.
4.Which equation is a cubic function with a negative leading coefficient?
- y = 4x³ − 2x + 1
- y = −2x³ + x² + 5
- y = x² − 6x + 2
- y = 7x − 3
Applications
Apply function models to situations and explain your reasoning.
5.A toy rocket’s height above the ground is modelled by h(t) = −4t² + 16t + 3, where h is in metres and t is in seconds. Find its height at launch, the time when it reaches its maximum height, and that maximum height.
6.Choose the most suitable function type for each situation: (a) savings that earn compound interest at a fixed percentage; (b) distance covered when travelling at a constant speed; (c) the area of a square in relation to its side length. Choose from linear, quadratic, or exponential.
- Savings growing by compound interest at a fixed percentage
- Distance at a constant speed
- Area of a square compared with its side length
- Exponential
- Linear
- Quadratic
7.Explain why an exponential model could be suitable for a city’s population when the population grows by roughly the same percentage each year. Include how the model’s growth relates to the current population.
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