Quadratic Functions

  Vertex Form of Quadratic Functions

The function f(x)=a(x-h)^2 + k is called the vertex form of a quadratic function. 

 

Because the vertex is translated  h horizontal units and k vertical units from the origin then the vertex of the parabola  is (h,k)

Effect of (k) on the quadratic function

Effect of (h) on the quadratic function

(k) represents the vertical translation 

k > 0 the graph shits up

k < 0 the graph shifts down

Effect of (a) on the quadratic function

                (h) represents the horizontal translation 

                  h > 0 the graph shits right

                  h < 0 the graph shifts left

(a) affects the direction and the shape of the parabola

|a| > 1 the parabola is narrower

|a| < 1 the parabola is wider

a < 0 the parabola opens down