Algebra 2 domain

Question

A golfer shanks the ball at tee off, causing the ball to veer directly towards the parking lot. One unlucky vehicle is sitting 1010 feet away but directly in line with the path of the ball. The vehicle has a 1.5 foot tall window beginning at 2 feet off the ground. The total height of the vehicle is 6 feet.

The path of the ball is represented by the function, f(x) = –0.0004x² + 0.4067x + 0.167, where x represents the horizontal distance in feet the ball has traveled in the air.

Determine the appropriate domain, to the nearest foot, for the distance actually traveled in the air by the ball, whether the ball hits the car, and if the window will be smashed.

(a) 0 ≤ x ≤ 1010, the ball strikes the vehicle a little more than 3 feet below the window, thereby limiting the distance the ball travels.

(b) 0 ≤ x ≤ 1010, the ball smashes the window of the vehicle

(c) 0 ≤ x ≤ 1017, the ball, te ball flies over the vehicle, missing by less than 12 inches

(d) 0 ≤ x ≤ 1010, the ball strikes the vehicle more than 6 inches above the window, thereby limiting the distance the ball travels

Answer 1

The bottom of the window is at height 2 [y = 2].

The top of the window is at height 3.5 [y = 3.5].

I used a graphing utility (zoom, trace, box) to find that when y = 3.5, x ≈ 1008, and when y = 2, x ≈ 1012.

Did you draw a picture? What picture did you draw??

If the car is in position to be hit [side facing the golfer], then the window gets smashed because the distance given, 1010' is between 1008 & 1012. That is, as the ball goes from 0' to 1012' horizontally, it hits the glass at 1010' (choice b).

But, if the car is facing the golfer, then the ball hits the hood...

I'm not trying to add to your confusion, but these are valid points. See what your teacher says.