Question

If f(x)=(x+1)(x-2)(x-3) represents a student's displacement from school in
kilometers, where x is measured in minutes, which of the following is an
accurate interpretation of the student's trip?
a) The student starts 6 km from school, walks to school and arrives at school
after 2 minutes, continues walking to the playground, turns around, walks
back to the school and arrives after 3 minutes.
b) The student starts 6 km from school, walks to school and arrives at school
after 2 minutes, waits there for 1 minute, then returns home.
c) The student starts 6 km from school, walks to school and arrives at school
after 2 minutes, turns back to their house to the playground, turns around,
walks back to the school and arrives after 3 minutes.
d) The student starts 6 km from school, walks to school and arrives 1 minute
later, sits by the school, returns home, arrives after 2 minutes, and then turns
around and arrives back at school for a second time at 3 minutes.
e) None of the above are correct
It

Answer 1

A is the answer to your question

Answer 2

Displacement means the distance traveled on a straight line to get to a certain destination. The interpretation of the given equation is option (a):

Given that:

$f(x) = (x + 1)(x - 2)(x - 3)$

First, we calculate how far the student traveled to arrive at the school.

This means that we calculate f(0).

So, we have:

$f(0) = (0 + 1)(0 - 2)(0 - 3)$

$f(0) = ( 1)( - 2)( - 3)$

$f(0) = 6$

The student walked 6km to school

When x = 2, it means:

$f(x) = (x + 1)(x - 2)(x - 3)$

$f(2) = (2 + 1)(2-2)(2 -3) = 0$

This means that the student got to school after 2 minutes

When x = 3, it means

$f(x) = (x + 1)(x - 2)(x - 3)$

$f(3) = (3 + 1)(3-2)(3 -3) = 0$

This means that the student walked away, turned back and got to school after 3 minutes.

From the given options, option (a) fits the above description.

Read more about speed, displacement and time at:

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