Question

A rocket is launched in the air. The graph below shows the height of the rocket

h in feet after t seconds. What is the rocket’s greatest height?

Answer 1

Answer:(19, 1768.9).

Explanation:

It is defined as the graph of a quadratic function that has something bowl-shaped.

(x - h)² = 4a(y - k)

(h, k) is the vertex of the parabola:

a = √[(c-h)² + (d-k²]

(c, d) is the focus of the parabola:

It is given that:

The graph of the parabolic path is shown in the picture.

From the graph:

The x-coordinate of the vertex is (38, 0)

The x-coordinate represents time in seconds

The y-coordinate of the vertex is (19, 1768.9)

The y-coordinate represents the height in meters

Thus, the x-coordinate of the vertex is (38, 0) a

Answer 2

The rocket's greatest height is 0 feet, reached after 22 seconds.

The graph depicts the height of the rocket launched in the air, with the x-axis representing time in seconds and the y-axis representing the height in feet.

We are asked to determine the greatest height achieved by the rocket, which translates to finding the maximum point of the quadratic function.

My analysis reveals that the function representing the rocket's height is -25t²+550t. To find the maximum height, we need to factor this expression and identify the vertex.

Steps to solve:

1. Factor the expression:

We can factor the expression using the common factor method:

-25t²+550t = -25(t²-22t)

2. Rewrite in factored form:

-25(t-22)t

Analysis:

The factored form reveals that the expression is a product of two linear factors, one containing (t-22) and the other containing t. The maximum value of the function occurs at the vertex, which is the point where these two factors are equal to zero.

Therefore, the greatest height of the rocket is reached when t = 22 seconds. This corresponds to a height of:

h = -25(22)² + 550(22)

h = -12100 + 12100

h = 0 feet

The rocket's greatest height is 0 feet, reached after 22 seconds.