HELP PLS MANY POINTS Use the function f(x) to answer the questions: f(x) = 4x2 + 8x − 5 Part A: What are the x-intercepts of the
graph of f(x)? Show your work. (2 points) Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points) Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 point
1 answer:
Answer:
see below
Step-by-step explanation:
f(x) = 4x^2 + 8x − 5
To find the x intercepts set y = 0
0 =4x^2 + 8x − 5
Factor
0=(2x-1)(2x+5)
Using the zero product property
2x-1 =0 2x+5 =0
2x=1 2x = -5
x = 1/2 x = -5/2
The x intercepts are ( 1/2 ,0) and ( -5/2,0)
Rewriting in vertex form by completing the square
4 ( x^2 + 2x) -5
4 ( x^2+2x +1) -4*1 -5
4 ( x+1) ^2 -9
Vertex form is
a( x-h) ^2 +k where ( h,k) is the vertex
The vertex is ( -1,-9)
We know it opens upwards since a > 0
Plot the vertex and the x intercepts
The graph is symmetric on based on the vertex
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Answer:
n=1705
Step-by-step explanation:
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Assuming the X follows a normal distribution
And the distribution for is:
We know that the margin of error for a confidence interval is given by:
(1)
The next step would be find the value of ,
and
Using the normal standard table, excel or a calculator we see that:
If we solve for n from formula (1) we got:
And we have everything to replace into the formula:
And if we round up the answer we see that the value of n to ensure the margin of error required mm is n=1705.