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What is the best way to estimate the solution of a quadratic equation?
Wiki User
∙ 11y ago
I don't think there is any easy way to estimate it; just use the quadratic equation to calculate the solutions. You can round some of the numbers to get an estimate; in this case you might even do most of the calculation in your head, but it's probably easier just to do the full calculation.
Wiki User
∙ 11y ago
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How are quadratic equations used in real life?
Many real life physics problems are parabolic in nature. Parabolas can be shown as a quadratic equation. If you have two variables then usually you can use the equation to find the best solution to a problem. Also, it is a beginning in the world of mathematical optimization. Some equations use more than two variables and require the technique used to solve quadratics to solve them. I just ran an optimization of 128 variables. To understand the parameters I needed to set I had to understand quadratics.
What is the special cases of quadratic equation?
The standard form of a quadratic equation is: ax^2 + bx + c = 0. Depending on the values of the constants (a, b, and c), a quadratic equation may have 2 real roots, one double roots, or no real roots.There are many "special cases" of quadratic equations.1. When a = 1, the equation is in the form: x^2 + bx + c = 0. Solving it becomes solving a popular puzzle: find 2 numbers knowing their sum (-b) and their product (c). If you use the new Diagonal Sum Method (Amazon e-book 2010), solving is fast and simple.Example: Solve x^2 + 33x - 108 = 0.Solution. Roots have opposite signs. Write factor pairs of c = -108. They are: (-1, 108),(-2, 54),(-3, 36)...This sum is -3 + 36 = 33 = -b. The 2 real roots are -3 and 36. There is no needs for factoring.2. Tips for solving 2 special cases of quadratic equations.a. When a + b + c = 0, one real root is (1) and the other is (c/a).Example: the equation 5x^2 - 7x + 2 = 0 has 2 real roots: 1 and 2/5b. When a - b + c = 0, one real roots is (-1) and the other is (-c/a)Example: the equation 6x^2 - 3x - 9 = 0 has 2 real roots: (-1) and (9/6).3. Quadratic equations that can be factored.The standard form of a quadratic equation is ax^2 + bx + c = 0. When the Discriminant D = b^2 - 4ac is a perfect square, this equation can be factored into 2 binomials in x: (mx + n)(px + q)= 0. Solving the quadratic equation results in solving these 2 binomials for x. Students should master how to use this factoring method instead of boringly using the quadratic formula.When a given quadratic equation can be factored, there are 2 best solving methods to choose:a. The "factoring ac method" (You Tube) that determines the values of the constants m, n, p, and q of the 2 above mentioned binomials in x.b. The Diagonal Sum Method (Amazon ebook 2010) that directly obtains the 2 real roots without factoring. It is also considered as "The c/a method", or the shortcut of the factoring method. See the article titled" Solving quadratic equations by the Diagonal Sum Method" on this website.4. Quadratic equations that have 2 roots in the form of 2 complex numbers.When the Discriminant D = b^2 - 4ac < 0, there are 2 roots in the form of 2 complex numbers.5. Some special forms of quadratic equations:- quadratic equations with parameters: x^2 + mx - 7 + 0 (m is a parameter)- bi-quadratic equations: x^4 - 5x^2 + 4 = 0- equations with rational expression: (ax + b)/(cx + d) = (ex + f)- equations with radical expressions.
Can quadratic systems be solved using elimination and substitution?
You can solve lineaar quadratic systems by either the elimination or the substitution methods. You can also solve them using the comparison method. Which method works best depends on which method the person solving them is comfortable with.
Which is the best equationof a line of best fit this scatterplot?
A straight line equation
Application of differential equation in chemistry?
The rate at which a chemical process occurs is usually best described as a differential equation.
What are the best on-line calculators for solving quadratic equations by using the quadratic formula?
Trywww.mathsisfun.com/quadratic-equation-solver.html
Why use quadratic formula?
Using the quadratic formula to solve any quadratic equation is the best way of getting around it because the quadratic formula is "the opposite of b plus or minus the square root of b squared minus 4ac all divided by 2a. This formula only works with trinomials and second degree equaitons. If the equation is a binomial, then put in a placeholer (0) and substitute them into the equation.
Is 3x - 2 equals -3x2 a quadratic equation?
Yes. (Assuming that -3x2 is the best representation of 3x2 that this browser will allow.)
Where can someone find information on quadratic equation solvers?
If you are looking to download an app on your ti-84 or higher calculator, you should watch the "Quadratic Formula Program on the Ti-84" on youtube. Best of Luck!
How do you do the Quadratic formula?
The general form of a quadratic equation is ax^2+bx+c=0. The quadratic formula is used to find the x intercepts of a parabola. It goes like this: x=(-b+or-the (square root of b^2-4ac))/2a. With a specific equation you plug the values for a, b, and c into the formula. It is best to use a graphing calculator. Hope this helps.
How do you find a solution to a 2 step equation?
The best way is: One step at a time.
How are quadratic equations used in real life?
Many real life physics problems are parabolic in nature. Parabolas can be shown as a quadratic equation. If you have two variables then usually you can use the equation to find the best solution to a problem. Also, it is a beginning in the world of mathematical optimization. Some equations use more than two variables and require the technique used to solve quadratics to solve them. I just ran an optimization of 128 variables. To understand the parameters I needed to set I had to understand quadratics.
What equation would provide the best estimate of 32 percent of 44.7?
44.7 * .32
Which statement best explain why there is no real solution to the quadratic equation 2x2 plus x plus 7 equals 0?
The discriminant says; b^2 - 4ac 1^2 - 4(2)(7) = 1 - 56 < 1 So, less than 1 and no real roots
What values best approximate the solutions of -4x2 plus 7x plus 5 equals 0?
Using the quadratic equation formula:- x = -0.5447270865 or x = 2.294727086
How does a quadratic model differ from linear model?
LinearIn a linear model, the plotted data follows a straight line. Every data point may not fall on the line, but a line best approximates the overall shape of the data. You can describe every linear model with an equation of the following form:y = mx + bIn this equation, the letter "m" describes the angle, or "slope," of the line. The "x" describes any chosen value on the horizontal axis, while the "y" describes the number on the vertical axis that corresponds to the chosen "x" value.QuadraticIn a quadratic model, the data best fits a different type of curve that mathematicians call quadratic. Quadratic models have a curved shape that resembles the letter "u." You can describe all quadratic models with an equation of the form:Y = ax^2 + bx + cAs with linear models, the "x" corresponds to a chosen value on the horizontal axis and "y" gives the correlating value on the vertical axis. The letters "a," "b" and "c" represent any number, i.e., they will vary from equation to equation
How is quadratic equation used today?
In reality the quadratic equation as many functions in the scientific and mathematical world. The equation is used to find shapes, circles, ellipses, parabolas, and more. The quadratic formula looks a little menacing, however it is not . The quadratic equation is different from the formula and looks like this: and we will be discussing the quadratic equation. The quadratic equation is used to find the curve on a Cartesian grid. It is primarily used to find the curve that objects take when they fly through the air. For example a softball, tennis ball, football, baseball, soccer ball, basketball, etc. It also used to design any object that has curves and any specific curved shape needed for a project. The military uses the quadratic equation when they want to predict where artillery shells hit the earth or target when fired from cannons. So if your goal is to go into the military and work with artillery or tanks, you will be using the quadratic equation on a daily basis. Other uses of the quadratic equation include explaining how planets in our solar system revolve around the sun. Our planets were initially tracked by early scientists, who did not have the advantage of computers, and they used the quadratic equation to determine how planets in our solar system do not have circular orbits - they have elliptical orbits. Newton also based his laws of motion on the quadratic equation by defining the acceleration of objects and forces that act upon them. He based his laws on objects falling and moving, taking into consideration the objects are on a spinning object (earth), which is orbiting the our sun. Newton was not aware of the forces that act on our solar system from the rotation of the Milky Way Galaxy. Do you think this would have mad a difference in his calculations? No the answer would still be the same; however it would have taken him longer to calculate. The quadratic equation is used by car makers to determine how much and what type of brakes are needed to stop a car going at various speeds, while it is still on the drawing boards. This and other design functions which use the quadratic equation are part of the design steps of a new car, truck, motorcycle, and other types of automobiles. When a police officer investigates a car accident scene, he/she uses the quadratic equation in their efforts to determine what velocities the cars when traveling when the collision occurred. Also, who was at fault and why the vehicles were damaged the way they were. These calculations are also used by car designers to develop an even safer care for occupants during future collisions. The quadratic equation is used in the design of almost every product in stores today. The equation is used to determine how safe products are and the life expectancy of products, such as when they can expect to quit working. Designers can then see what needs to be changed in the product to make it last longer. Another area that the quadratic equation is helpful is in the design of sound systems, such as: speakers and electronic circuits for vibrating the speakers. Speakers send out sound waves and these sound waves vibrate or resonate, sometimes causing unwanted cancellations of sound waves. Designers use this equation to redesign the circuits and speakers so sound waves reinforce each other and do not cancel each other out for the best sound quality. The quadratic equation has many practical applications in the world beyond school. You may not think you need to know it now; however the higher paying jobs go to those who can use the quadratic equation to design safe and useful products for people.
