What is a Quadratic Equation?A quadratic equation is a polynomial equation that has an exponent of 2. This means that the highest exponent in the equation is 2. A quadratic equation can be written as: ax2 + bx + c = 0 where a, b, and c are constants. In general, what this might mean is that the equations have either one or two "squared" terms with x as their variable or there are no squared terms but all three terms have exponents of 2 (see Quadratic Formula). These equations can either look like y = x2, 3x = 2x - 3, 4y + 12 = 0, etc.The distinguishing feature of a quadratic equation that produces a simple curve is that the graph of the equation is either a parabola (the shape of a projectile such as a cannonball) or a hyperbola (a U-shaped curve). For example, consider the equation y = x2. The graph of this equation looks like an upside-down parabola. If the coefficient of the term with x2 is negative, then the graph appears as a hyperbola, for example y = -x2.Another way to see what a quadratic equation is is to consider it as two simultaneous linear equations in two variables. For example, the equation y = 3x + 4 describes a parabola. If you change the fourth term of this equation to x2, the graph still looks like a parabola. What does this mean? Here are two points of view on the same graph:It is important to understand that although some equations can give many different shapes, some equations are only able to describe one specific shape. For example, neither y = x2 nor y = -x2 can describe a hyperbola or any other 3-dimensional curve because they cannot be graphed as two separate linear equations in 2 variables. What are the Factors of a Quadratic Equation?The factors of a quadratic equation are the constants in an equation that can be used to factorize or rewrite the expression in terms of binomials. For example, y = -x2 is a quadratic equation because it can be written as (-x)·(-x) which is written as (-1)(-1). (-1)(-1) can be rewritten as x-x or just x.For example, if y = -(2+x), then y can be factored by seeing how many times x is in the expression.
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