Without plotting any points other than intercepts, draw a possible graph of the following polynomial:
2 answers:
The first thing to do is find the x-intercepts of the function so that you can plot them. Set the function f(x) to zero and find the values of x.
0 = <span>(x + 8)3(x + 6)2(x + 2)(x − 1)3(x − 3)4(x − 6)
There are 6 intercepts:
x+8=0 ---> x= -8
x+6=0 ---> x=-6
x+2=0 ---> x=-2
x-1=0 ---> x=1
x-3=0 ---> x=3
x-6=0 ---> x=6
The 6 intercepts are plotted as shown in the picture. The tool I used was Microsoft Excel. This is one possible sketch of the graph. The trend could move in any ways as long as it passes these 6 intercepts.</span>
0 = <span>(x + 8)3(x + 6)2(x + 2)(x − 1)3(x − 3)4(x − 6)
There are 6 intercepts:
x+8=0 ---> x= -8
x+6=0 ---> x=-6
x+2=0 ---> x=-2
x-1=0 ---> x=1
x-3=0 ---> x=3
x-6=0 ---> x=6
The 6 intercepts are plotted as shown in the picture. The tool I used was Microsoft Excel. This is one possible sketch of the graph. The trend could move in any ways as long as it passes these 6 intercepts.</span>
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Answer:
Check the explanation
Step-by-step explanation:
One way ANOVA
The null and alternative hypothesis for this one way ANOVA is given as below:
Null hypothesis: H0: There is no significant difference in the averages of the scores for the quizzes, exams and final only.
Alternative hypothesis: There is a significance difference in the averages of the scores for the quizzes, exams and final only.
The ANOVA table with calculations can be seen in the attached images below:
In the attached image below, we get the p-value for this one way ANOVA test as 0.0221. We do not reject the null hypothesis if the p-value is greater than the given level of significance and we reject the null hypothesis if the p-value is less than the given level of significance or alpha value.
In the attached image below, we are given that the p-value = 0.0221 and level of significance or alpha value = 0.05, that is p-value is less than the given level of significance. So, we reject the null hypothesis that there is no significant difference in the averages of the scores for the quizzes, exams and final only. This means we conclude that there is a significance difference in the averages of the scores for the quizzes, exams and final only.
Answer:
The graph is possible for
Step-by-step explanation:
we know that
The discriminant of a quadratic equation of the form
is equal to
If D=0 the quadratic equation has only one real solution
If D>0 the quadratic equation has two real solutions
If D<0 the quadratic equation has no real solution (complex solutions)
In this problem , looking at the graph, the quadratic equation has two real solutions (the solutions are the x-intercepts)
so
therefore
The graph is possible for