Quadratic equation

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A quadratic equation graphed in the coordinate plane.

A quadratic equation is an equation in the form of ax2 + bx + c, where a is not equal to 0. It makes a parabola (a "U" shape) when graphed on a coordinate plane. It is the simplest polynomial equation.

The Quadratic Formula[change | change source]

The quadratic formula is a formula used to find the points where the graphed equation crosses the x-axis, or the horizontal axis. These points are called the "zeroes" of a function. The formula is:

Where the letters are the corresponding numbers of the original equation, ax2 + bx + c = 0. Also, a cannot be 0 for the formula to work properly.

The factored form of this equation is y = a(xs)(xt), where s and t are the zeros, a is a constant, and y and the two xs are ordered pairs which satisfy the equation.

Proof[change | change source]

The quadratic formula is proved by completing the square,

Divide the quadratic equation by a :

Move c/a:

Use the method of completing the square

To "complete the square" is to find some "k" so that:
for some y.

Add to both sides of the equation:

Which gives:

The left side is now a perfect square; it is the square of

The right side can be a single fraction, with a common denominator 4a2.

Find the square root of both sides.

Move b/2a:

Other websites[change | change source]