Algebra/Chapter 9/Graphing

Algebra

A Quadratic function is a polynomial where the highest power is two. The basic form of this function is: F(X) = ax² + bx + c. Where, ax² is the quadratic term, bx is the linear term and c is the independent term or "constant", which does not depend on the variable, x. The letters a and b are called "coefficients", a being the "leading coefficient". The standard form is F(X) = ax² + bx + c. The x-intercepts of the function are:

$x={\frac {-b+{\sqrt {b^{2}-4ac}}}{2a}}$ OR $x={\frac {-b-{\sqrt {b^{2}-4ac}}}{2a}}$

The independent term is also the y-coordinate of the point of intersection with the y-axis (when X=0, F(X)=C).

A quadratic function has a "vertex" or "turning point", which is the point where the function has either a maximum or minimum value. If a is greater than zero, then there will be a minimum and the curve will be concave. If a is less than zero, then there will be a maximum and the curve will be convex. If a = 0, then we have a linear function rather than a quadratic function.The x-coordinate of the vertex is $x=-{\frac {b}{2a}}$ The y-coordinate of the vertex is $F(-{\frac {b}{2a}})$

The general form of a quadratic equation is actually F(X) = ax² + bxy + cy² + dx + ey + f = 0, which can take many shapes including circles, ellipses and parabolas, but in most Western high schools, quadratic equation refers only to those of the form F(X) = ax² + bx + c, which forms a parabola.