I’d really appreciate it if anyone can help me answer these questions. I’m stuck.

Question

f(x) models the flight of the rocket in feet.

Blue Bombers: f(x) = 81 – x^2

1. How high is the rocket when it explodes?

2. How many seconds was the rocket in the air before it exploded? 3. How many seconds did the sparkles stay in the air?

4. What method did you use to solve the given equation?

5. Show your work below:

Red Rockets: g(x) = –2x^2 + 29x – 90

1. How high is the rocket when it explodes?

2. How many seconds was the rocket in the air before it exploded?

3. How many seconds did the sparkles stay in the air?

4. What method did you use to solve the given equation?

5. Show your work below.

Green Gammas: k(x) =-x^2 + 12x - 15

1. How high is the rocket when it explodes?

2. How many seconds was the rocket in the air before it exploded?

3. How many seconds did the sparkles stay in the air?

4. What method did you use to solve the given equation?

5. Show your work below.

Orange Orthogonals: h(x) = –6x^2 +53x – 91

1. How high is the rocket when it explodes?

2. How many seconds was the rocket in the air before it exploded?

3. How many seconds did the sparkles stay in the air?

4. What method did you use to solve the given equation?

5. Show your work below.

Answer 1

How high is the rocket when it explodes?

This is asking what is the y-value of the vertex (the maximum). To find the vertex, put the equation +in ax²+bx+c = 0 form.

x = -b/(2a) gives you the x-value of the vertex (how long it takes to reach the highest point when it explodes)

Plug in the answer you get for x in the equation for x and solve for y. This is the max height.

How many seconds before it explodes?

This is asking for the x-value of the vertex, which we solved for above in order to find the y-value.

How many seconds did the sparkles stay in the air?

Basically this is asking when did it reach the ground. The height of the ground is 0, so set the equation equal to 0 and solve for x (see more info below). The answer is going to be the positive value, never the negative one, as negative time doesn't make sense in these problems.

What method did you use to solve the given equation?

For Q3, there are different methods you can use. If there's only an x² term,(e.g., blue) you can solve for x by isolating x² and then taking the square root. If there is both an x² term and an x term then you can try to factor it or use the quadratic equation. Or you can use a graphing calculator to graph the equations and use trace to find the x-intercepts.

Let me know if you still have questions.