Question

The height of a satellite above Earth over a certain period of time is described by the function shown.

f(x)=2x2−16x+800
In this function, x = the time in hours and f(x) = the height in kilometers. What is the minimum height of the satellite during this period of time?

Answer 1

Explanation:

To find the minimum height of the satellite during the given time period, we need to find the vertex of the parabolic function f(x) = 2x^2 - 16x + 800.

The vertex of a parabola with equation f(x) = ax^2 + bx + c is given by the formula:

x = -b / 2a and f(x) = -b^2 / 4a + c

In this case, a = 2, b = -16, and c = 800. Substituting these values into the formula, we get:

x = -(-16) / 2(2) = 4

f(x) = -(-16)^2 / 4(2) + 800 = 848

Therefore, the minimum height of the satellite during the given time period is 848 kilometers, and it occurs after 4 hours of flight time.