Algebra 1: Modeling with Quadratic Functions

A ball is thrown into the air from the ground. The ball's height over time can be modeled with a quadratic function. The table shows the time, t, in seconds, and the height of the ball, h, in feet. Using the intercepts from the table, the factored form of the quadratic function can be written as f(t) = at(t - 4).

-The quadratic function that models the scenario is f(t) = -4 t²+ 16t. -After 2 seconds, the ball attains its maximum height of 16 feet.

Consider the quadratic function that has x-intercepts of -1 and -7 and passes through the point (-2, -20). What is the value of a in the factored form of this function? -20=a(-2+1)(2-7)

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Finish the steps below to write a quadratic function for the parabola shown.1. Use the vertex form, f(x) = a(x - h)2 + k, and substitute in the values for h and k.f(x) = a(x - 5)2 + 3 2. Use another point and substitute in values for x and f(x). Solve for a. 5 = a(6 - 5)2 + 3 3. 5 = a(6 - 5)2 + 3 3. Write the function, using the values for h, k, and a.

The function f (x)= 2(x-5)²+3

A company produces remote-controlled helicopters. The company's profit, in thousands of dollars, as a function of the number of helicopters produced per week can be modeled by a quadratic function. When 1 helicopter is produced per week, the company's profit is 4 thousand dollars. The maximum profit, 22 thousand dollars, occurs when 4 helicopters are produced per week. The function that models the scenario, where h is the number of helicopters produced per week, is f(h) = -2(h - 4)2 + 22.

When 6 helicopters are produced weekly, the company's profit is thousand dollars. (plug 6 in for h)

A company produces remote-controlled helicopters. The company's profit, in thousands of dollars, as a function of the number of helicopters produced per week can be modeled by a quadratic function. When 1 helicopter is produced per week, the company's profit is 4 thousand dollars. The maximum profit, 22 thousand dollars, occurs when 4 helicopters are produced per week. If h is the number of helicopters produced per week, which function models the scenario?

f(h) = -2(h - 4)2 + 22