Answer:
A. h(x) = -\frac{1}{200}(x - 60)^2 + 20
B. the height of the arrow after it has flown a distance of 100 meters is 12 meters.
Explanation:
A) Writing the quadratic function to represent the height of the arrow as a function of its distance:
Let's use the vertex form of a quadratic function:
y = a(x - h)^2 + k
where:
(h,k) is the vertex of the parabola
a is a constant that determines the shape of the parabola
We know that the vertex of the parabola is at (60,20), since the arrow reached its maximum height of 20 meters after it has flown a distance of 60 meters.
To find the value of a, we can use the fact that the arrow starts at a height of 2 meters. This means that the point (0,2) is on the parabola.
2 = a(0 - 60)^2 + 20
2 = 3600a + 20
-18 = 3600a
a = -\frac{1}{200}
Therefore, the quadratic function that represents the height of the arrow as a function of its distance is:
h(x) = -\frac{1}{200}(x - 60)^2 + 20
B) Determining the height of the arrow after it has flown a distance of 100 meters:
To find the height of the arrow after it has flown a distance of 100 meters, we simply need to plug x=100 into the quadratic function we found in part A:
h(100) = -\frac{1}{200}(100 - 60)^2 + 20
h(100) = -\frac{1}{200}(40)^2 + 20
h(100) = 12
Therefore, the height of the arrow after it has flown a distance of 100 meters is 12 meters.