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Solving Quadratic Equations and Graphing Squares

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Section 8.2
#12 solve each equation by using the quadratic formula (what is this quadratic formula? Don't understand how this is done)
M^2 + 2m = 8

#20 Solve each equation by using the quadratic formula
4 + 20x = 25x^2

#28 solve each equation by using the quadratic formula
2y^2 + 1 = 2y

#42 Number solutions. Find b^2 - 4ac and the number of real solutions to each equation
9m^2 + 16 = 24m

#50 ½ x^2 + x = 1

#80 Find two real numbers that have a sum of 8 and a product of 2

Section 8.3
#6 Writing a quadratic equation with given solutions. For each given pair of numbers find a quadratic equation with integral coefficients that has the numbers as its solutions.
-8, 2

#24 Using the discriminant in factoring. Use the discriminant to determine whether each quadratic polynomial can be factored, then factor the ones that are not prime.
8x^2 + 6x - 27

#32 Equations Quadratic in form
(3a + 2)^2 - 3(3a + 2) = 10

#54 Find all real solutions to each equation
2x - 5√x + 2 = 0

Section 9.1
#10 Linear and constant functions. Graph each function and state its domain and range.
G(x) = x + 2

#20 Absolute value functions. Graph each absolute value function and state its domain and range.
F(x) = | x - 2|

#34 Quadratic functions. Graph each quadratic function and state its domain and range
Y = -2x^2 + 3

#38 square root functions. Graph each square root function and state its domain and range
F(x) = √x + 1

#56 Graphing relations. Graph each relation and state its domain and range
X = -3

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Section 8.2
#12 solve each equation by using the quadratic formula (what is this quadratic formula? Don't understand how this is done)
m^2 + 2m = 8
Solution. m^2 + 2m - 8 =0

By the formula, we get

So,
or

#20 Solve each equation by using the quadratic formula
4 + 20x = 25x^2
Solution: The equation can be rewritten as 25x^2-20x-4=0
So,
So, or

#28 solve each equation by using the quadratic formula
2y^2 + 1 = 2y
Solution. 2y^2 + 1 = 2y 2y^2 -2y + 1 = 0
Since , it has no real solutions.

#42 Number solutions. Find b^2 - 4ac and the number of real solutions to each equation
9m^2 + 16 = ...

Solution provided by:
Changping Wang, MA
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"
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