Math Problem Statement

Help

Student Messaging Open options Avatar Brandon Howard 10th Grade ASSESSMENT Question Id : 614484 1

2

3

4

5

6

7

8

9

10

Exit 5 of 105 of 10 Items 03:50

Skip to resources Question A discus was thrown from a height 5 feet above the ground. The graph shows the height in feet of the discus above the ground as a quadratic function of x, the horizontal distance in feet the discus traveled.

What is the domain of the function for this situation? Responses A 0 ≤ y ≤ 530 ≤ y ≤ 53 B 5 ≤ y ≤ 535 ≤ y ≤ 53 C 5 ≤ x ≤ 2305 ≤ x ≤ 230 D 0 ≤ x ≤ 2300 ≤ x ≤ 230 Skip to navigation

© Progress Learning 2025, All Rights Reserved. Terms | Privacy PHONE 1-877-377-9537 | FAX 1-877-816-0808 Blog

Solution

In this situation, the height of the discus is represented as a quadratic function of the horizontal distance traveled. To find the domain of the function, we are looking for the range of possible values for x, which is the horizontal distance the discus traveled.

Since the graph represents a projectile motion, the domain corresponds to the horizontal distance over which the discus is in the air, starting from when it is thrown to when it hits the ground.

  • The height of the discus starts at 5 feet (initial height) and decreases as it travels horizontally until it hits the ground. The distance it travels horizontally before hitting the ground is represented by the end of the graph.

The domain of the function will be the interval of x (horizontal distance), which typically starts at x = 0 and goes up to the point where the discus reaches the ground (where the height equals 0).

Based on the information provided in the options:

  • Option D (0 ≤ x ≤ 230) seems the most likely, as the horizontal distance ranges from 0 feet (starting point) to 230 feet (where the discus hits the ground).

Correct Answer: D (0 ≤ x ≤ 230)

Would you like a more detailed explanation or further assistance with a similar problem?

Here are some related questions:

  1. How can we calculate the maximum height of the discus from the quadratic equation?
  2. What type of equation best models projectile motion like this one?
  3. How do you determine the vertex of a parabola in projectile motion?
  4. Why does the height of the discus start at 5 feet in this scenario?
  5. What is the significance of the x-intercept in a projectile motion graph?

Tip: When analyzing projectile motion graphs, remember that the domain corresponds to the horizontal distance traveled, and the range corresponds to the height of the object.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Projectile Motion
Quadratic Functions
Domain of a Function

Formulas

Quadratic function formula
Projectile motion formula (height vs. distance)

Theorems

Domain of a quadratic function
Projectile motion principles

Suitable Grade Level

Grade 10