Graphing, Parabolas and Quadratic Equations
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Please see the attached file for the fully formatted problems.
Sample #1
Sample #2
Sample #3
Find the roots of the quadratic equation:
.
(If there is more than one root, separate them with commas.)
Sample # 4
Solve the equation
for .
(If there is more than one solution, separate them with commas.)
Sample # 5
Solve where is a real number.
Simplify your answer as much as possible.
(If there is more than one solution, separate them with commas.)
Sample #6
Solve the following equation for by using the quadratic formula:
.
(If there is more than one solution, separate them with commas.)
Sample #7
Sample # 8
Find all real or imaginary roots of .
(If there is more than one root, enter additional roots with the or icon.)
Sample #9
Find the -intercept(s) and the coordinates of the vertex for the parabola . If there is more than one -intercept, separate them with commas
Sample # 10
Graph the parabola:
.
To graph the parabola, plot the vertex and four additional points, two on each side of the vertex, and then click on the graph icon.
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Solution Summary
Graphing, Parabolas and Quadratic Equations are investigated.
Education
- BSc , Wuhan Univ. China
- MA, Shandong Univ.
Recent Feedback
- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"
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