Math Homework - Desklib

Running head: MATH HOMEWORK 1
Math Homework
Name
Institution

MATH HOMEWORK 2
Math Homework
Question 1
A quadratic function has a series of varying positive gradients on one part and a series of varying
negative gradients on the other part. The positive and negative gradients meet at a point where
the gradient is zero hence forming a maximum point or a minimum point. The model in part C
has a negative gradient in the range −4 ≤ x ≤ 0. That is,
0−3
−2−−4 =−1.5 ,∧−1−0
0−−2 =−0.5
Additionally, the model has a series of varying positive gradients in the range 2 ≤ x ≤14.
3−0
4−2 =1.5 , 8−3
6−4 =2.5 , 15−8
8−6 =3.5 ... 48−35
14−12 =6. 5
The rates of change, −1.5 ,−0.5 ,1.5 , 2.5 , 3.5 , ... ,6.5 can be represented using a schematic
diagram resembling that of a quadratic function as shown in figure 1.1.
Figure 1.1: The schematic model

MATH HOMEWORK 3
Therefore, table C can be modelled as a quadratic function.
Question 2
part a
Using the quadratic regression function in Desmos graphing calculator we obtain the result
shown in figure 1
Therefore, y=−0.0057 x2+0.0984 x+ 49.5357
Part b
a describes the direction the quadratic model opens (up or down). That is, the trend of the
number of worms as the number of days’ increases. In this case, the negative value of a denotes a
decrease in the number of worms with the increase in the number of days. b describes the
coefficient of the linear term of the model and shows how the number of worms is linearly to the
number of days. On the other hand, c describes the initial number of worms.
Part c