Question

a golfer hits a golf ball. the graph of ( h(t) ) below shows the height of the ball over time.
interpret the meaning of the vertex in this situation.
the golf ball reaches a maximum height of ( square ) feet after ( square ) seconds.
interpret the meaning of the horizontal intercepts in this situation.
when the golf ball was hit, it was ( square ) feet above the ground.
the ball lands after ( square ) seconds.
practical domain: ( square leq t leq square ) seconds
practical range: ( square leq h(t) leq square ) feet

Explanation:

Step1: Analyze the vertex

The vertex of a parabola (which this graph resembles) gives the maximum or minimum value. In the context of height over time for the golf - ball, the vertex gives the maximum height. Looking at the graph, the \(y\) - coordinate (height) of the vertex is \(120\) feet and the \(x\) - coordinate (time) is \(4\) seconds.

Step2: Analyze the horizontal intercepts

The horizontal intercepts (where \(H(t)=0\)):

• When \(t = 0\), \(H(0)=0\) (the ball is on the ground when it is hit).
• When \(t = 8\), \(H(8)=0\) (the ball lands).

Step3: Determine the practical domain

The practical domain is the set of all valid input values (time \(t\)). The ball is in motion from \(t = 0\) (when it is hit) to \(t = 8\) (when it lands). So, \(0\leq t\leq8\).

Step4: Determine the practical range

The practical range is the set of all valid output values (height \(H(t)\)). The minimum height is \(0\) (when it is on the ground at \(t = 0\) and \(t = 8\)) and the maximum height is \(120\) (from the vertex). So, \(0\leq H(t)\leq120\).

Answer:

• The golf ball reaches a maximum height of \(120\) feet after \(4\) seconds.
• When the golf ball was hit, it was \(0\) feet above the ground.
• The ball lands after \(8\) seconds.
• Practical Domain: \(0\leq t\leq8\) seconds
• Practical Range: \(0\leq H(t)\leq120\) feet