3.6: Quadratic FUNctions

QUADRATIC FUNCTIONS are those funky-looking curved graphs with equations that have multiple xs and confusing exponents in them.

A function f is a QUADRATIC FUNCTION if and only if it fits in the form where a, b, and c are real numbers with a not equal to zero.

What can you figure out from a QUADRATIC FUNCTION?

a: if positive, the funtion opens up; negative, the funtion opens down

it controls the width of the graph

b: controls how the vertex moves along the inversion of the function

c: the y intercept

VERTEX: The minimum or maximum value of the function (minimum if a>0; maximum if a<0)

The coordinate of the vertex of a parabola is

AXIS OF SYMMETRY: That dotted line down the middle of the parabola that runs through the VERTEX.

on the right is the STANDARD FUNCTION

of a parabola with Vertex V(h,k)

You can make your ugly QUADRATIC EQUATION into a fashionable STANDARD EQUATION by simply completing the square, as demonstrated on the right.