Answer:
The balloon was thrown at a height of 3 feet above the ground.
The balloon reached its maximum height of 6 feet above the ground one second after it was thrown.
The balloon hit the ground 2.414 seconds after it was thrown.
Explanation:
Definition of the variables:
- x is the time (in seconds) after the water balloon is thrown.
- y is the height (in feet) of the water balloon above the ground.
The y-intercept tells us the value of y when x is zero. Therefore, it tells us the height of the water balloon above the ground at the time the balloon was thrown. So the water balloon was 3 feet above the ground when it was thrown.
The vertex (1, 6) is the maximum point of the curve.
- The y-value of the vertex tells us the maximum height the water balloon reached.
- The x-value of the vertex tells us the time the water balloon reached its maximum height.
Therefore, the balloon reached its maximum height of 6 feet above the ground one second after it was thrown.
The roots are the points at which the curve intersects the x-axis, so when y is zero. They tell us the time when the balloon's height is zero, so when it is at ground level.
One of the roots is negative, so as time cannot be negative, the root x = -0.414 can be discounted.
The other root x = 2.414 tells us that the balloon hit the ground 2.414 seconds after it was thrown.