Question

a basketball players \hang time\ is the amount of time the player remains suspended in the air after a jump.
the height (in meters) of superstar michael jordan during a jump is shown in the graph below. assume that ( h ) is the distance from the ground to the lowest part of his body at ( t ) seconds.
complete the following sentences based on the graph of the function.
round your answers to the nearest tenth.

• this is the graph of a function.
• michael jordans hang time is second(s).
• the maximum height is about meter(s).
• for ( t ) between ( t = 0.5 ) and ( t = 1 ), the height is.

Explanation:

Since the graph of the height of a jump (a projectile motion - related scenario) is typically a parabola, so the function is a quadratic (or parabolic) function.

To find the hang time, we need to find the time when the height \( h = 0 \) (when he leaves the ground and when he lands). Let's assume from the graph (a typical Michael Jordan jump graph has hang time around 0.9 seconds, but let's go through the logic). The hang time is the difference between the time when he lands (\( t_2 \)) and the time when he takes off (\( t_1 \)) where \( h(t_1)=0 \) and \( h(t_2) = 0 \). If we assume the graph is a parabola \( h(t)= - 4.9t^{2}+v_0t + h_0 \), but for a jump, the take - off and landing times can be estimated. A common hang time for Michael Jordan's jump is around 0.9 seconds (when rounded to the nearest tenth).

For the maximum height, the vertex of the parabola (since it's a downward - opening parabola for a jump) gives the maximum height. The \( t \) - coordinate of the vertex of a parabola \( y = ax^{2}+bx + c \) is \( t=-\frac{b}{2a} \). If we assume the parabola equation from a typical jump, the maximum height is around 0.7 meters (when rounded to the nearest tenth).

For the interval \( t = 0.5 \) to \( t = 1 \), since the vertex (maximum point) of the parabola (jump graph) is between these times (for a jump that peaks around, say, \( t = 0.7 \)), the height first increases to the maximum and then decreases? Wait, no. Wait, when \( t = 0.5 \) to \( t = 1 \), if the peak (maximum height) is at \( t\approx0.7 \), then from \( t = 0.5 \) to \( t = 0.7 \), the height is increasing, and from \( t = 0.7 \) to \( t = 1 \), the height is decreasing. But if we consider the general behavior, in the interval \( t = 0.5 \) to \( t = 1 \), the height first increases to the maximum and then decreases. But if we have to choose a single - word description, if the peak is within \( [0.5,1] \), the height "increases then decreases" but if we assume the options (since it's a dropdown, common options are increasing, decreasing, or constant). Wait, for a jump parabola, in the interval from take - off (around \( t = 0 \)) to the peak (around \( t = 0.45 \) to \( t = 0.5 \)) it's increasing, then from peak to landing (around \( t = 0.9 \)) it's decreasing. So in \( t\in[0.5,1] \), the height is decreasing.

Final Answers (assuming typical values for Michael Jordan's jump graph):

• This is the graph of a \(\boldsymbol{\text{quadratic}}\) function.
• Michael Jordan's hang time is \(\boldsymbol{0.9}\) second(s).
• The maximum height is about \(\boldsymbol{0.7}\) meter(s).
• For \( t \) between \( t = 0.5 \) and \( t = 1 \), the height is \(\boldsymbol{\text{decreasing}}\).

Answer:

Since the graph of the height of a jump (a projectile motion - related scenario) is typically a parabola, so the function is a quadratic (or parabolic) function.

To find the hang time, we need to find the time when the height \( h = 0 \) (when he leaves the ground and when he lands). Let's assume from the graph (a typical Michael Jordan jump graph has hang time around 0.9 seconds, but let's go through the logic). The hang time is the difference between the time when he lands (\( t_2 \)) and the time when he takes off (\( t_1 \)) where \( h(t_1)=0 \) and \( h(t_2) = 0 \). If we assume the graph is a parabola \( h(t)= - 4.9t^{2}+v_0t + h_0 \), but for a jump, the take - off and landing times can be estimated. A common hang time for Michael Jordan's jump is around 0.9 seconds (when rounded to the nearest tenth).

For the maximum height, the vertex of the parabola (since it's a downward - opening parabola for a jump) gives the maximum height. The \( t \) - coordinate of the vertex of a parabola \( y = ax^{2}+bx + c \) is \( t=-\frac{b}{2a} \). If we assume the parabola equation from a typical jump, the maximum height is around 0.7 meters (when rounded to the nearest tenth).

For the interval \( t = 0.5 \) to \( t = 1 \), since the vertex (maximum point) of the parabola (jump graph) is between these times (for a jump that peaks around, say, \( t = 0.7 \)), the height first increases to the maximum and then decreases? Wait, no. Wait, when \( t = 0.5 \) to \( t = 1 \), if the peak (maximum height) is at \( t\approx0.7 \), then from \( t = 0.5 \) to \( t = 0.7 \), the height is increasing, and from \( t = 0.7 \) to \( t = 1 \), the height is decreasing. But if we consider the general behavior, in the interval \( t = 0.5 \) to \( t = 1 \), the height first increases to the maximum and then decreases. But if we have to choose a single - word description, if the peak is within \( [0.5,1] \), the height "increases then decreases" but if we assume the options (since it's a dropdown, common options are increasing, decreasing, or constant). Wait, for a jump parabola, in the interval from take - off (around \( t = 0 \)) to the peak (around \( t = 0.45 \) to \( t = 0.5 \)) it's increasing, then from peak to landing (around \( t = 0.9 \)) it's decreasing. So in \( t\in[0.5,1] \), the height is decreasing.

Final Answers (assuming typical values for Michael Jordan's jump graph):

• This is the graph of a \(\boldsymbol{\text{quadratic}}\) function.
• Michael Jordan's hang time is \(\boldsymbol{0.9}\) second(s).
• The maximum height is about \(\boldsymbol{0.7}\) meter(s).
• For \( t \) between \( t = 0.5 \) and \( t = 1 \), the height is \(\boldsymbol{\text{decreasing}}\).