This song represents loneliness and solituhd, which are common emotions of the human condition. Through the whole song, singer is waiting in her chair and is filled with despair. She remembers about someone she is deeply in love with, but someone is gone. She feels sadness and gloom everywhere. Also she is staring outside and feels she could go mad with her despair. She wants to get her love back. I think she could have divorced with her husband or broken up with her boyfriend, or her husband was dead. Many people can feel isolation or solitude in many different cases. In additional, people need other people’s love or attention, which can help them overcome their difficult emotions. Therfore, this song’s theme is how the feeling of solitude can lead people to very depressed feelings becauses we feel unconnected or distant from others. Whether situation is death or break up, many people feel the unhappines of solitude.
5.1 solving quadratic inequalities in one variable.
This part solves the quadratic inequalities on number line. Also, we find x values and domain.
To solve quadratic inequality follow these step.
The real solutions to the equation become boundary points for the solution to the inequality.
Make the boundary points solid circles if the original inequality includes equality; otherwise, make the boundary points open circles.
Select points from each of the regions created by the boundary points. Replace these “test points” in the original inequality.
If a test point satisfies the original inequality, then the region that contains that test point is part of the solution.
5.5Solving Systems of Equations Algebraically
This section uses substitution.
Make both equations into “y =” format.
Set them equal to each other.
Simplify into “= 0” format (like a standard Quadratic Equation)
Solve the Quadratic Equation!
Use the linear equation to calculate matching “y” values, so we get (x,y) points as answers.
4.5 Equivalent forms of the equation of a quadratic function.
An equation of a quadratic function in standard, y=a(x-p)^2+q, can be expanded and written in general form, y=ax^2+bx+c. When the equation of a quadratic function is in general form, most characteristics of the graph cannot be identified. For the reason, it is useful to be able to convert from general form to standard form. This can be done by “completing the square”. This process involves including a perfect square in the equation of the quadratic function.
4.7 Modelling and solving problems with quadratic functions
This chapter is use of chapter 4.1~4.6 technology. Some problems can be solved by writing, then graphing a quadratic function.
To factor a number means to break it up into numbers that can be multiplied together to get the original number.
In order to solve quadratic equations by factoring. We should set he equation to equal zero. Secondly, Factor the non-zero side. Thirdly, use the zero factor property to set each factor equal to zero. Fourthly, solve each factor. Fifthly, reject extraneous(undefined) roots. Lastly, check the solution in the orginal equation!!
Using square roots to solve quadratic equations
In order to solve a quadratic equation by completing the square(using roots). We should write the equation such that the variable terms are on the left side and the constant term is on the right side. Secondly, divide the coefficient of x by 2 and square it. Thirdly, add this square value to both left and right side f the equation. Fourthly, write the left side of the equation as a perfect square binomial. Lastly, use the square root property!!
Multiply the coefficients. The coefficients are the numbers outside of a radical. …
Multiply the numbers inside the radicals. After you’ve multiplied the coefficients, you can multiply the numbers inside the radicals. …
Simplify the product.
I learned multiplying Radical Expression in pre-cal11 class. When I see this part first, I thought it will make me die. However, Ms.Burton’s solve method made me different. I could feel solve these questions easily. So now, if test questions give me about multiplying radical questions,I can get a 100% score.