What are the coordinates of the vertex of the graph of f(x)=4|x+6|? Enter your answer as an ordered pair without parentheses in
the box.
( )
( )
2 answers:
The vertex of the graph is the point at which the function changes from decreasing to increasing.
Note that
- for all
the function is decreasing;
- for all
the function is increasing;
- at
the function has zero and this point is the point at which the function changes from decreasing to increasing.
Since at the function has zero, then
This means that vertex has coordinates (-6,0).
Answer: (-6,0)
You might be interested in
Answer:
Step-by-step explanation:
a) to create a scatter plot for the data, let data for clinics be x and that one for Bowling alleys be y then plot x values with corresponding y values on a graph tool.
<u>x y</u>
14 12
1 3
6 6
5 7
10 7
6 8
11 9
8 15
6 7
16 12
The scatter plot is attached below
b) a cluster is a group of data that is close together. From the plot, the ordered pairs forming a cluster are;
(6,6), (6,7), (5,7), and (6,8)
c) An outlier is a point in a plot which lies very far from the other values. In this case, point its point (8,15)
d)The linear regression equation is one written in the form of
Y=a+bX where ;
Y=the dependent variable
X=the explanatory variable
a=the intercept, which is the value of y when x=o
b=slope of the line
The formula to apply here is ;
a=(∑y)(∑x²)-(∑x)(∑xy) / n(∑x²)-(∑x)² where n is number of samples
b= n(∑xy)-(∑x)(∑y) / n(∑x²)-(∑x)²
Form a table like below
<u>x y xy x² y²</u>
14 12 168 196 144
1 3 3 1 9
6 6 36 36 36
5 7 35 25 49
10 7 70 100 49
6 8 48 36 64
11 9 99 121 81
8 15 120 64 225
6 7 42 36 49
16 12 192 256 144
83 86 813 871 850------------sum
∑x=83 ∑y=86 ∑xy=813 ∑x²=871 ∑y²=850 and n=10
Applying the formula
a=(∑y)(∑x²)-(∑x)(∑xy) / n(∑x²)-(∑x)²
a=[(86 * 871) - (83*813) ]/ 10 (871-83²)
a=[74906 - 67479] / 10(-6018)
a=[7427] / -60180
a= - 0.1234
b= n(∑xy)-(∑x)(∑y) / n(∑x²)-(∑x)²
b=10(813)-(83*86) / 10 (871)-(83²)
b=[8130-7138] / 8710 -6889
b= 992/1821
b=0.5448
The liner regression equation will be;
Y=a+bX
Y= -0.1234 + 0.5448 X
e) correlation coefficient r is given by;
r= n∑xy - (∑x)(∑y) / √n(∑x²)-(∑x)² × √n(∑y²)-(∑y)²
r=10*813 - (83*86) / √10 *871 -83² ×√10*850 - 86²
r=8130-7138 / √8710-6889 × √8500-7396
r= 992 / (√1821 × √1104)
r=992/ 42.67×33.23
r=992/1417.9
r=0.6996
f) r² is important because it shows you the proportion of the variance of one variable that is predictable from the other variable.
r=0.6996
r²=0.6996² =0.4894
