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For instance, mathematically, the square cannot have more than four sides but it is uncertain about their existence to form what is defined as an object called “a square”. Also, in mathematics, numbers are defined as a value, or an amount, represented by unique symbols, digits. There are two types of numbers, real number which exists on the number line and complex number or as defined as “imaginary number” which is outside of the number line. Real numbers are accepted as a simple idea where their properties can be proven using logic and reasoning, while for imaginary number or “i” cannot exists on the number line because square-root of a negative number is irrational, yet Cardano, an Italian mathematician, had a discussion on the cubic equations with the lack of the proper, real solution. The theory on imaginary number explains that though it does not exist on the number line, or what is applied to define the value of each digit, yet it is proven to exist. Similarly, it is possible to determine existence of the…

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assignment. After reviewing the upcoming lessons and considering the timeline, we agreed that I would teach the students about coordinate planes, including the parts of the plane, how to plot points, find the distance between points, and reflect points across axes. The timing of this topic is fitting since the students just completed a unit on number lines, integers, and rational numbers. State, District, and National Standards Met The two AZ College and Career Readiness Standards, found on the…

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A parabola will always have a domain of all x-values so I immediately knew that the domain of this quadratic equation is all real numbers, or (?∞,∞). To find the range, I evaluated the (h,k) which in this equation is (1/4, 15/8). I can see that this parabola has a minimal value of 15/8 and go up to positive infinity. The range is y is greater than or equal to 15/8, or y. The maximum/minimum value can be found by the output of the quadratic function at the vertex. By evaluating the vertex in…

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Grade-Level Introduction As students are gaining their formal educational experience, the emphasis in mathematics in fourth grade continues to develop and target Number and Operations, Algebraic Reasoning and Algebra, Geometry and Measurement, and Data and Probability. Many essential components addressed in fourth grade will encompass real world experiences that naturally pique the student’s problem solving skills, engage reasoning and communication with others, provide a powerful and positive…

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I think, overall, that my lesson went well. My lesson plan was focused on students building off their previous knowledge of solving quadratics to understand complex solutions of quadratics. For this lesson I started off by allowing students to solve a quadratic I had written on board. However the quadratic equation I had written on the board was the wrong equation so students got stuck when they tried to use the quadratic equation because they got a negative under the square root. From there, we…

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affecting the equation, which is gravity, and in represents the distance from the vertex to the origin. Notice that gravity had to be converted in order to keep all units consistent throughout the equation, shown in work. After plugging in the appropriate information, shown on work, we find the position x and position y equations. The position x will be called PX(t) and the position y equation will be called PY(t). The sixth step is to take the newly found PY(t) equation and solve for t using…

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solve. An important rule to understand when deriving the quadratic formula by completing the square, is that the leading term must equal to “1”. On the other hand, if the leading term does not equal to “1”, one will have to factor the equation by dividing each term by the leading term. The quadratic equation must start as the following: 〖ax〗^2+bx+c=0. Next, the constant number is to be moved to the other side of the equation. Another important rule in math is that whenever a number is moved,…

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however, the discovery of Eris, an object in space, led astronomers to debate the validity of Pluto as a planet. Thus, it came to be known as a plutoid, and not a planet. This incident, insignificant as it may seem, goes to show how even NASA, one of the top scientific organizations in the world, may second guess their own ideology. If it not had been for the discovery of Eris, whos to say that Pluto would not have remained as a planet to this day? New discoveries and evidence, beneficiary as…

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Two people that spoke out against his teaching were his idols Henri Poincare and Leopold Kronecker. With Kronecker even go as far as to public opposition and personal attacks, saying that Cantor was “renegade” along with becoming a “corrupter of youth.” These thoughts is because Kronecker believes that algebraic numbers are countable, and that were numbers that are transcendental are uncountable. Around this time in 1884, Cantor would face depression for the first time until the end of his life.…

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The zeros are where the graph crosses the X axis. These zeros are also known as the solutions or the roots. The types of zeros that functions can have are rational zeros, irrational zeros, or complex zeros. Rational zeros are just the basic integers. Irrational zeros have radicals that can’t be removed. Complex zeros have imaginary numbers. Out of these 3 types of zeros, a quartic function can only have 4 rational/irrational zeros, 2 rational/irrational zeros and 2 complex zeros, or 4 complex…

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