Quadratic function

completing the square only works with quadratic functions, otherwise the equation will not be able to 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, the sign changes. In this case the constant “c” is positive, and later changed as “-c” when moved to the right side of the equation. As a result, it should look like the…

In order to derive the Quadratic Formula by completing the square, it was important to verify that the quadratic equation was in standard form which is ax? + bx + c = 0. By using this correct form, I prevented myself from using the wrong values for a,b, or c which could result in an incorrect solution. I began by rewriting the equation by subtracting c to the other side which isolated ax? + bx. I divided the equation by a because it was multiplied on the squared term. In addition, I took the…

Francisco Gutierrez 03.03 Linear Functions 1. The equation we have is 2x+3y=1200. The first thing you would need to do in the equation is subtract 2x to both sides. 2x cancels out and now we subtract 2x and 1200. You would end up getting 3y=2x-1200. Then finally, you would have to divide everything by -3. Your final answer for this question is y=-2/3x+400. Your slope is -2/3 and your y-intercept is 400. 2. So we know that our slope is -2/3 and the y-intercept is 400. You have one point on the…

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The Result With full data sheet of Rampo Valley Reservation park and Harriman State Park, we determine the relative density, frequency, relative frequency, relative dominance and important value. <Table 1> is Ramapo Valley Reservation Park’s table . <Table 2> is Harriman State Park’s table. Relative density is percentage of number of individual of one species by sum of the individuals of all species. Relative frequency is percentage of frequency by sum of the frequencies of all…

To ensure an athlete may return to play as soon as possible, a variety of rehabilitation processes should be implemented. These should include progressive mobilisation, graduated exercise (including stretching, conditioning and total body fitness), training and the use of hot and cold applicants. When each step is correctly addressed, it will increase the likelihood of a speedy reintroduction to sport. Progressive mobilisation is necessary to enhance the range of movement available. A…

Fundamental Theorem of Calculus The Fundamental Theorem of Calculus evaluate an antiderivative at the upper and lower limits of integration and take the difference. This theorem is separated into two parts. The first part is called the first fundamental theorem of calculus and states that one of the antiderivatives of some function may be obtained as the integral of the function with a variable bound of integration. The second part of the theorem, called the second fundamental theorem of…

John Gutmann was one of America’s most distinctive photographers. Gutmann was born in Germany where he became an artist. He later fled Germany due to the Nazi’s because he was a Jew. Gutmann moved to San Francisco and re-established himself as a photojournalist captivating the lives of Americans. He mainly took photographs of people who were imperfect like himself because of his Jewish nationality. Gutmann targeted the poor, circus folk, the gay community and the rich. Two of Gutmann’s works are…

The fundamental theorem of Calculus: The fundamental theorem of calculus asserts the interrelated properties of integration and differentiation. It says that a function when differentiated, can be brought back by integrating (anti-derivative) or a function when integrated, can be brought back by differentiation. First theorem: Let f be a function that is integrable on [a,x] for each x in [a,b], then let c be such that a≤c≤b and define a new function A as follows, A(x)=∫_c^x▒f(x)dt, if a≤x≤b.…

the equation & based off what I did I'm assuming that his possible answer came out not to be an real answer to his problem & that is mainly because the equation itself is not true when eighty one is inserted for the letter x in the default problem. Okay so basically for this particular problem we have to think of f of x as basically the y value if that makes sense. So this would mean that if you use addition for the number two & + to the letter y we will see the function go up by two. The…