Functions in Context Worksheets Grade 9

1. Liam is designing a parabolic arch for a bridge. The arch's height above the ground is modeled by the function h(x) = -0.02x² + 1.2x, where x is the horizontal distance in meters from the left support and h(x) is the height in meters. What is the maximum height of the arch above the ground?
2. Noah is tracking the height of a rocket launched from a platform. The height h(t) in meters after t seconds is modeled by the function h(t) = -5t² + 41t + 6. What does the value h(6) represent in this context?
3. Matiu is analyzing the water level in a reservoir during a drought. The water volume V(t) in millions of liters is modeled by the quadratic function V(t) = -0.4t² + 8t + 120, where t represents the number of days since the drought began. Interpret the meaning of V(15) and calculate its value.

…and 5 more problems

1. Liam is designing a parabolic arch for a garden bridge. The arch follows the function h(x) = -0.5x² + 4x, where h(x) represents the height in meters above the ground at a horizontal distance x meters from the left support. What is the maximum height of the arch above the ground?
2. A right triangle is drawn on a coordinate plane with vertices at (0,0), (6,0), and (6,8). A circle is circumscribed around this triangle such that all three vertices lie on the circle's circumference. What is the area of this circumscribed circle? (Use π = 3.14)
3. Isabella is a civil engineer designing a suspension bridge. The main cable's height above the bridge deck, in meters, is modeled by the quadratic function h(x) = 0.002x² - 0.48x + 36, where x is the horizontal distance in meters from the left tower. Interpret the meaning of h(120) in the context of this problem, and then calculate and state the value of h(120).

…and 5 more problems

1. The function h(t) = -5t² + 45t models the height in meters of a ball thrown by Aroha after t seconds. What does h(3) represent and what is its value?
2. Mere is tracking the height of a plant in her science experiment. The height h(t) in centimeters after t days is modeled by the function h(t) = 2.5t + 15. What does h(10) represent in this context, and what is its value?
3. A drone is flying over a park following a parabolic path modeled by the function h(t) = -2t² + 12t + 5, where h represents the drone's height in meters and t represents time in seconds. At what time does the drone reach its maximum height, and what is that maximum height?

…and 5 more problems