The quadratic equation often crops up in the context of area. In a culture that was primarily based on agriculture, the area of farmland owned, traded etc was vitally important.
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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.
You'll typically use it when solving a quadratic equation - when factoring isn't obvious.
The quadratic equation has multiple real-world applications throughout engineering. One of which is modeling ballistic arcs and trajectories as in the path of bullet or projectile.
Quadratic form is a shorthand term generally used to say to put an equation in the form ax2 + bx + c .
Translate to what? I assume you need help interpreting it. The quadratic equation is used to solve the quadratic polynomial, ax2 + bx + c = 0, where a, b, and c can be any number. For example, if you need to solve the equation x2 = 5 + 2x, you first convert it into the standard form mentioned above: x2 - 2x - 5 = 0. Now find the coefficients, a, b, and c. In this case, a = 1, b = -2, c = -5. Finally, you replace these coefficients in the quadratic equation. The "plus-minus" sign simply means that the quadratic equation is a shortcut for two equations - one in which you add, the other in which you subtract, the terms at the top. The solutions given by the quadratic equation are values of "x" that satisfy the equation.