To write a quadratic function that models the path of the rocket, we use the standard form of a quadratic equation:
f(x) = a(x - h)^2 + k
where h and k are the x and y coordinates of the vertex, and a is a coefficient that determines the shape of the parabola.
We are given that the maximum height of the rocket is 36 feet, which means the vertex is (10, 36). Therefore, h = 10 and k = 36.
We are also given that the rocket lands on the ground at the point (20, 0). This gives us another point on the parabola that we can use to solve for a.
Substituting x = 20 and y = 0 into the equation, we get:
0 = a(20 - 10)^2 + 36
0 = 100a + 36
-36 = 100a
a = -0.36
Now that we have a, we can write the quadratic function in standard form:
f(x) = -0.36(x - 10)^2 + 36
To graph this function, we can use a calculator or plotting software. Here's a graph of the function:
Quadratic function graph
As we can see from the graph, the rocket follows a parabolic path, reaching a maximum height of 36 feet at x = 10, and landing on the ground at x = 20.
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Answer:
To write a quadratic function that models the path of the rocket, we use the standard form of a quadratic equation:
f(x) = a(x - h)^2 + k
where h and k are the x and y coordinates of the vertex, and a is a coefficient that determines the shape of the parabola.
We are given that the maximum height of the rocket is 36 feet, which means the vertex is (10, 36). Therefore, h = 10 and k = 36.
We are also given that the rocket lands on the ground at the point (20, 0). This gives us another point on the parabola that we can use to solve for a.
Substituting x = 20 and y = 0 into the equation, we get:
0 = a(20 - 10)^2 + 36
0 = 100a + 36
-36 = 100a
a = -0.36
Now that we have a, we can write the quadratic function in standard form:
f(x) = -0.36(x - 10)^2 + 36
To graph this function, we can use a calculator or plotting software. Here's a graph of the function:
Quadratic function graph
As we can see from the graph, the rocket follows a parabolic path, reaching a maximum height of 36 feet at x = 10, and landing on the ground at x = 20.