Question

ball reaches a maximum height force of gravity brings it back down to the ground ball shot from cannon the vertex is the maximum height the parabola opens downwards the x - axis is counting by 1s and therefore the ball lands in about 3.0 seconds the y - axis is counting by 0.5s and therefore the ball reaches its maximum height at about 7.0 feet the leading coefficient for this function would be positive

Explanation:

Step1: Analyze the vertex

The vertex of a parabola represents the maximum or minimum point. In the context of the ball's height (where it reaches the highest point), the vertex is the maximum height.

Step2: Determine the direction of the parabola

Since the ball goes up and then comes down (due to gravity), the parabola opens downwards.

Step3: Analyze the x - axis

If the x - axis is counting by 1's and looking at the point where the ball lands (the right - hand x - intercept), it is about 3.0 seconds.

Step4: Analyze the y - axis

If the y - axis is counting by 0.5's and looking at the vertex (maximum height), it is about 7.0 feet.

Step5: Determine the leading coefficient

For a parabola \(y = ax^{2}+bx + c\), if it opens downwards, \(a<0\). But there is an error here. Since the parabola opens downwards, the leading coefficient should be negative.

Answer:

The vertex is the maximum height. The parabola opens downwards. The ball lands in about 3.0 seconds. The ball reaches its maximum height at about 7.0 feet. The leading coefficient for this function should be negative (there is an error in the given "positive" option).