Hi, I have attached a problem I would like help with as a picture file. It's not a difficult assignment, but I tend to make "stupid" or careless mistakes when it comes to the more "simple" things, so I would greatly appreciate your help so that I can check my work after I finish and see if I did it correctly and/or identify any mistakes I made. The first part of the picture is a thorough description of the experiment and how to do the problem, and at the bottom of the picture, you will find the data set that I am supposed to use to complete it.

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The solution is attached below in two files. the files are identical in content, only differ in format. The first is in MS Word format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you. ...

Solution Summary

The solutions shows in detail how to construct the system of equations for least-square fit of a quadratic polynomial.

Given the parabola y = -(x - 6)2 - 1, determine each of the following.
7. Identify whether the parabola y = -(x - 6)2 - 1 opens up or down.
8. Identify the vertex of the parabola y = -(x - 6)2 - 1.
9. Identify the x-intercept(s) of the parabola y = -(x - 6)2 - 1.
10. Identify the y-intercept(s) of the parabola y

Use completing the square to rewrite the equation in one of the standard forms for a conic and identify the conic.
1) x2 + 12x - y + 30 = 0
Find the equation of the parabola determined by the given information.
2) Vertex at the origin, focus at (0, 3)
Find the equation of the hyperbola.
3) Vertices at (0, 8) and (0, -8), fo

Give the focus, directrix, and axis for each parabola:
1. x^2= 1/8y
Write an equation for each parabola with vertex at the origin:
1. through (-2, -2 square root 2), opening left
2. through (2,-4), symmetric with respect to the y-axis

(1) Write an equation for the parabola with vertex at (4,0) and y-intercept at (0,4). How many x-intercepts does the graph have?
(2) Find the equation for a parabola that has a vertex at (-12,-40) and passes through the point (6,68).

Find the equation of the parabola with focus (3, -1) and directrix y = 5.
A) x=-1/4(y+1)^2+3
B) x=-1/4(y+1)^2+4
C) y=-1/12(x-3)^2+2
D) y=-1/12(x-3)^2-1

First Part:
What is the discriminant? Explain what information the discriminant gives us and why this information is important. What does the discriminant tell us about the graph of a quadratic equation?
Second Part:
What is a parabola and where does it come from? What important information is given by the vertex of a p