B) D-
The graph below describes the journey of a bus between two stops.
81
a) Work out the
6
acceleration, in m/s?,
in the first 20 s.
c)
S=
Velocity in m/s)
2
b) Work out the distance
between the two stops.
0
0
20
40
60 80 100 120 140 160 180
Time (t in seconds)
c) Work out the average
speed of the bus during
the journey
Give your answer to 1 d. p.
Velocity-Time Graphs
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Overview

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step-by-step explanation:

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

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

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.