It looks like you have an image of a math assignment related to quadratic functions. Let me go through the questions step by step and help you solve them:

1) Write the vertical position equation for Rudy's rocket.

The problem provides the equation for the rocket’s vertical position, which is given as:

$h(t) = -16t^2 + 120t + 2$

This equation represents the height (h) of the rocket at any given time (t), with the acceleration due to gravity being -16 feet per second squared, an initial velocity of 120 feet per second, and an initial height of 2 feet.

2) Fill in the following table of values using the trace button on your calculator.

The table corresponds to values of $t$ (time) and $h(t)$ (height). You need to calculate the height $h(t)$ at each time step:

Use the equation $h(t) = -16t^2 + 120t + 2$ to calculate the values of $h(t)$ at these specific times. You can use a calculator for this.

3) What does the $h(t)$ value mean when $t = 12$?

When $t = 12$, substitute this into the equation to find $h(12)$:

$h(12) = -16(12)^2 + 120(12) + 2$

This will give you the rocket's height at 12 seconds after launch. You’ll interpret that value in the context of the rocket's motion—whether it’s on the way up, at its peak, or coming back down.

4) What is the maximum height this rocket can reach? How long does it take the rocket to reach this height?

The maximum height occurs at the vertex of the parabola described by the quadratic function. The formula for the time at the vertex is:

$t = \frac{-b}{2a}$

For the equation $h(t) = -16t^2 + 120t + 2$, $a = -16$ and $b = 120$, so the time is:

$t = \frac{-120}{2(-16)} = 3.75 \text{ seconds}$

Substitute this time into the equation to find the maximum height $h(3.75)$.

5) What is the y-intercept of the function? Write the y-intercept in function notation and explain what it means in terms of the problem situation.

The y-intercept occurs when $t = 0$, which is already given as $h(0) = 2$. This means that at the moment of launch, the rocket is 2 feet above the ground.

6) What does $h(t) = 0$ mean in the context of the rocket?

When $h(t) = 0$, it means that the rocket has hit the ground. Solve $h(t) = 0$ to find the time when this happens. This is the time when the rocket's height is zero after launch.

7) When does $h(t) = 0$ occur?

Solve the equation $h(t) = 0$, or $-16t^2 + 120t + 2 = 0$. This is a quadratic equation that you can solve using the quadratic formula:

$t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Where $a = -16$, $b = 120$, and $c = 2$.

8) At what time is the rocket 150 feet in the air?

Set $h(t) = 150$ and solve for $t$. This will tell you the time(s) at which the rocket is 150 feet above the ground.

9) What does the point (5.5, 7) mean in terms of the problem situation?

The point $(5.5, 7)$ represents the time (5.5 seconds) and the height (7 feet) of the rocket. In context, it means that at 5.5 seconds, the rocket is 7 feet above the ground.

Would you like to go through the detailed solutions for each of these steps? Let me know if you want further clarification or help solving any part of this!