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Graph-Equation Matching Exercise

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Graph-Equation Matching Exercise

Mathematical graphs and equations illustration

📊 Part 1: Graph-Equation Matching

Instructions: Match each graph description on the left with its corresponding equation on the right by drawing lines between them. Each graph has exactly one matching equation.

Graphs

A. Straight line passing through (0,3) with gradient 2
B. Parabola opening upward with vertex at (0,-4)
C. Exponential curve starting at (0,1) and increasing rapidly
D. Cubic curve passing through origin with positive leading coefficient
E. Horizontal line at height 5
F. Parabola opening downward with vertex at (2,8)

Equations

1. y = 5
2. y = x³
3. y = 2x + 3
4. y = x² - 4
5. y = 2ˣ
6. y = -(x - 2)² + 8

🔍 Part 2: Graph Feature Analysis

7. For the equation y = -3x² + 12x - 5, identify the following features:

a) y-intercept: ___________

b) Does the parabola open upward or downward? ___________

c) x-coordinate of the vertex: ___________

d) Maximum or minimum value: ___________

8. A population growth model is given by P(t) = 1000(1.05)ᵗ, where t is time in years.

a) Initial population: ___________

b) Growth rate per year: ___________%

c) Population after 10 years (to nearest whole number): ___________

9. Multiple Choice: Which equation represents a cubic function with a negative leading coefficient?

y = 2x³ + 5x - 1

y = -x³ + 4x² + 7

y = x² - 3x + 2

y = 3x + 4

🌍 Part 3: Real-World Applications

10. A ball is thrown upward and its height h (in metres) after t seconds is given by h = -5t² + 20t + 2.

a) What is the initial height of the ball? ___________ metres

b) At what time does the ball reach its maximum height? ___________ seconds

c) What is the maximum height reached? ___________ metres

11. Match each real-world scenario with the most appropriate type of function:

a) Bank account with compound interest ___________

b) Distance travelled at constant speed ___________

c) Area of a square garden vs. side length ___________

Options: Linear, Quadratic, Exponential

12. Explain why an exponential function would be appropriate for modelling population growth in a city:

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