There are an infinite number of different quadratic equations. The quadratic formula is a single formula that can be used to find the pair of solutions to every quadratic equation.
Because it is in the form of ax^2+bx+c=0 Because quadratic means squared hence ax squared + bx +c=0 has a squared number as it's highest term. This is in fact the area of a square of a side "x" is x^2, so every equation having variable with exponent 2 become quadratic equation.
The quadratic formula works for every quadratic equation because it is the standard form of a quadratic solved for x. ax2+bx+c=0 - Standard Form, how quadratic equations are normally displayed x2+bx/a+c/a=0 - Divide both sides by a, Division Property of = x2+(b/a)x= -(c/a) - Separate variables and constants, Subtraction Property of = x2+(b/a)x+(b/2a)2=(b/2a)2-(c/a) - Complete the square. (b/2)2 (x+b/2a)2=(b2-4ac)/4a2 - Factor and Simplify x+b/2a=+/-sqrt((b2-4ac)/4a2) - Square Root both sides. x=-(b/2a)+/-sqrt(b2-4ac)/2a - Solve for x, Subtraction Property of = x=(-b+/-sqrt(b2-4ac))/2a - The Quadratic Equation, Simplify
Answer It is due to the propensity of scholars of all types to label things of profound importance with words or modifications of words of a long dead language. In this case "quadratic" comes from the Latin "quadratus", meaning square. This is in fact the area of a square of a side "x" is x^2, so every equation having variable with exponent 2 become quadratic equation.
It tells us how many moles of every reactant and product there is in the equation.
Only if the discriminant of its equation is greater than zero will it have 2 different x intercepts.
The equation is true because of the reflexive property of equality which states in words that every quantity is equal to inself.
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.
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
Police, Quadratics, Action! If you know the initial speed of car, how far you are travelling and what your acceleration is, there is a special formula that lets you find out how long the journey will take. This formula is a quadratic with time as its unknown quadratic quantity. The police use this equation - along with many other quadratic and non-quadratic equations - when they attend a road traffic accident (RTA). They do this to find out if the driver was breaking the speed limit or driving without due care and attention. They can discover how fast the car was going at the time the driver started braking and how long they were braking for before they had the accident. This is done by finding the road's coefficient of friction and by measuring the length of the skid marks of the vehicles involved. Once they have this information they turn to Mathematics and the trusted quadratic equation. Einstein's Famous Quadratic The most famous equation in the world is technically quadratic. Einstein discovered the formula: Where E is the Energy of an object, m is its mass and c is the speed of light. This formula relates mass and energy and came from Einstein's work on Special and General Relativity. However, in practice it is not solved as a quadratic equation as we know the value of the speed of light. For more information on Einstein and his Theory of Special Relativity see the links at the bottom of the page. There are many more uses for quadratic equations. For more information please see the links to "101 Uses of a Quadratic Equation" at the bottom of the page.
Every quadratic equation has two solutions. If the quadratic expression that's equal to zero is a perfect square, then the two solutions are equal, and they look like one solution. Example: x2 - 6x + 9 = 0 (x - 3)(x - 3) = (x - 3)2 = 0 x = 3 and x = 3.