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- Quadratic equations
Key equations
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Key concepts
- Many quadratic equations can be solved by factoring when the equation has a leading coefficient of 1 or if the equation is a difference of squares. The zero-factor property is then used to find solutions. See
[link] ,
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[link] .
- Many quadratic equations with a leading coefficient other than 1 can be solved by factoring using the grouping method. See
[link] and
[link] .
- Another method for solving quadratics is the square root property. The variable is squared. We isolate the squared term and take the square root of both sides of the equation. The solution will yield a positive and negative solution. See
[link] and
[link] .
- Completing the square is a method of solving quadratic equations when the equation cannot be factored. See
[link]
.
- A highly dependable method for solving quadratic equations is the quadratic formula, based on the coefficients and the constant term in the equation. See
[link] .
- The discriminant is used to indicate the nature of the roots that the quadratic equation will yield: real or complex, rational or irrational, and how many of each. See
[link]
.
- The Pythagorean Theorem, among the most famous theorems in history, is used to solve right-triangle problems and has applications in numerous fields. Solving for the length of one side of a right triangle requires solving a quadratic equation. See
[link]
.
Section exercises
Verbal
When we solve a quadratic equation, how many solutions should we always start out seeking? Explain why when solving a quadratic equation in the form
we may graph the equation
and have no zeroes (
x -intercepts).
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When we solve a quadratic equation by factoring, why do we move all terms to one side, having zero on the other side?
We want to take advantage of the zero property of multiplication in the fact that if
then it must follow that each factor separately offers a solution to the product being zero:
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In the quadratic formula, what is the name of the expression under the radical sign
and how does it determine the number of and nature of our solutions?
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Describe two scenarios where using the square root property to solve a quadratic equation would be the most efficient method.
One, when no linear term is present (no
x term), such as
Two, when the equation is already in the form
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Algebraic
For the following exercises, solve the quadratic equation by factoring.
For the following exercises, solve the quadratic equation by using the square root property.
For the following exercises, solve the quadratic equation by completing the square. Show each step.
Questions & Answers
I'm interested in biological psychology and cognitive psychology
what does preconceived mean
How can I develope my cognitive domain
why is communication effective
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
please i need answer
Wekolamo
because it helps many people around the world to understand how to interact with other people and understand them well, for example at work (job).
Agreed 👍 There are many parts of our brains and behaviors, we really need to get to know. Blessings for everyone and happy Sunday!
ARC
A child is a member of community not society elucidate ?
Isn't practices worldwide, be it psychology, be it science. isn't much just a false belief of control over something the mind cannot truly comprehend?
compare and contrast skinner's perspective on personality development on freud
Skinner skipped the whole unconscious phenomenon and rather emphasized on classical conditioning
war
explain how nature and nurture affect the development and later the productivity of an individual.
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
and having a good philosophy of the world is like a sandwich and a peanut butter 👍
Jonathan
generally amnesi how long yrs memory loss
interpersonal relationships
What would be the best educational aid(s) for gifted kids/savants?
treat them normal, if they want help then give them.
that will make everyone happy
Saurabh
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Source:
OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
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