Question

2. Your fruit or vegetable will follow a parabolic path, where x is the horizontal distance it travels

(feet), and y is the vertical distance (feet).
a) The x-intercepts are the places where your fruit or vegetable is on the ground.
The first x-intercept is (0, 0).
The second x-intercept is where the fruit or vegetable hits the ground after it's launched.
What are the coordinates of the second x-intercept? (2 points: 1 point for each coordinate)

Answer 1

Since the x-intercepts are the points where the fruit or vegetable hits the ground, their y-coordinates are 0. We can find the x-coordinate of the second x-intercept by using the fact that the path of the fruit or vegetable is a parabolic curve.

If we assume that the launch point of the fruit or vegetable is at (a, b), where a is the horizontal distance it travels and b is the initial height, then the equation of the parabolic path can be written as:

y = ax^2 + bx

To find the second x-intercept, we need to solve for x when y = 0. Thus, we have:

0 = ax^2 + bx

Factoring out x, we get:

0 = x(ax + b)

Since the x-coordinate of the first x-intercept is 0, we know that a is not equal to 0. Therefore, the only way for the equation to be true is if x = 0 or ax + b = 0. We already know that x = 0 corresponds to the first x-intercept, so we solve ax + b = 0 for x:

ax + b = 0

x = -b/a

Therefore, the x-coordinate of the second x-intercept is -b/a.

The initial height b is not given in the problem, so we cannot determine the exact coordinates of the second x-intercept.