Quadratic function

◦ A function that can be written in the standard form◦ ax2 +bx+c◦ a is never “0”◦ Domain of the function is all real numbersQuadratic functions consist of a quadratic term, a linear

term, and a constant termThe quadratic term is the first term (square term)The linear term is the second term (x term)The constant term is the third term (number by

itself)

Linear functions have a linear term and a constant term only

Graph of a quadratic function

Parabola is the graph of a quadratic function It is a "U" shaped curve that may open up or down depending

on the sign of coefficient a. Maximum value has the function pointing down; a is negative Minimum value has the function pointing up; a is positive

Axis of symmetry is the line that divides a parabola into two parts that are mirror images Always a vertical line defined by the x-coordinate of the

vertex x=(the value of the coordinate) Each point on the parabola has a corresponding point on its

mirror image

Vertex of a parabola is the point at which the parabola intersects the axis of symmetry. It’s the turning point of the parabola It’s also the point at which you could fold the parabola along

the axis of symmetry and both parts of the parabola would look exactly the same

Examples of quadratic functions

f(x) = -2x2 + x - 1 opens down because a is negative

f(x) = x2 + 3x + 2 opens up because a is positive

a is positive opens upward

Vertex = (0,0)

Axis of sym: x=0