Graph Key Features Worksheets Grade 9

1. Nikau is studying the population P(t) = 290 * 2^(t/3) of bacteria in a lab experiment, where t is hours. From the graph of this function, identify the y-intercept and describe the interval(s) where the population is increasing or decreasing.
2. The population of a colony of bacteria is modeled by the function P(t) = 500 * 2^(t/3), where t is the time in hours and P(t) is the population size. After how many hours will the bacteria population reach 32,000?
3. Sophia graphs a quadratic function on a coordinate plane. The parabola opens downward and has its vertex at (7, 9). The graph also passes through the point (10, 0). Identify the x-intercepts of the function and state the interval(s) where the function is increasing.

…and 5 more problems

1. Matiu's function graph shows a parabola with vertex at (4, 15), x-intercepts at (1, 0) and (7, 0), and y-intercept at (0, 14). Identify the intervals where the function is increasing and decreasing.
2. A drone is flying over a park, and its height above ground is modeled by the function h(t) = -2t² + 12t + 5, where h is the height in meters and t is the time in seconds after launch. After how many seconds does the drone reach its maximum height?
3. f(x) = 2x² - 8x + 3; f(5) = ?

…and 6 more problems

1. Mere's function graph shows a parabola with vertex at (4, 8), x-intercepts at (2, 0) and (6, 0), and y-intercept at (0, 24). Identify the intervals where the function is increasing and decreasing.
2. Emma is analyzing the graph of f(x) = -3x² + 27x - 45. The graph has x-intercepts at (3, 0) and (5, 0), a y-intercept at (0, -45), and a vertex at (4.5, 15.75). Over what interval is the function increasing?
3. A drone is launched from a platform 20 meters high. Its height above ground is modeled by the function h(t) = -5t² + 15t + 20, where t is time in seconds and h(t) is height in meters. After how many seconds will the drone hit the ground?

…and 6 more problems