 Quadratic function ◦ A function that can be written in the standard form ◦ ax 2 +bx+c ◦ a is never “0” ◦ Domain of the function is all real numbers Quadratic functions consist of a quadratic term, a linear term, and a constant term The 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) = -2x 2 + x - 1 opens down because a is negative  f(x) = x 2 + 3x + 2 opens up because a is positive  a is positive  opens upward Vertex = (0,0) Axis of sym: x=0