The function \( h(x)=2 x+8 \) describes the height of a flock of flying birds (in feet above the ground) \( x \) seconds after they take flight. Use Desmos to find the intercepts (be sure you can also do this algebraically). The intercepts are: Explain in context what the intercept(s) of \( h(x) \) represent.

The function is h(x) = 2x + 8, where x is the time in seconds and h(x) is the height in feet. There are two intercepts to consider: 1. Y-intercept:  • Set x = 0:   h(0) = 2(0) + 8 = 8.  • So, the y-intercept is (0, 8). This point tells us that when the birds take flight (at time 0 seconds), they are 8 feet above the ground. 2. X-intercept:  • Set h(x) = 0 and solve for x:   2x + 8 = 0 → 2x = -8 → x = -4.  • So, the x-intercept is (–4, 0). Algebraically, this indicates that the line would cross the x-axis at x = –4 seconds. In the context of the problem, a negative time does not have a physical meaning because we start measuring the flight at time 0. However, mathematically it tells us that if the birds’ flight followed the same linear pattern before t = 0, they would have been at ground level 4 seconds before takeoff. Summary in context:  • The y-intercept represents the initial condition: at the moment of takeoff, the birds start 8 feet above the ground.  • The x-intercept, while not physically meaningful for the actual flight (since it occurs at a negative time), is the point where the extended line crosses the ground level (height 0 feet) before the birds took flight. These intercepts provide useful information about the function: the y-intercept describes the starting height, and the x-intercept, though not applicable in real time, shows where the extended behavior of the linear model would intersect the ground level.