The function is in the form: #a(x - h )^2 +k#
Where #h# is the axis of symmetry, and #k# is the maximum or minimum value of the function. This is known as the vertex of the parabola.
From example: vertex is at #( 2 , -7 )#
We now need to find roots and #y# axis intercept. This will then give us a sufficient number of plotting points.
Expand #y = ( x - 2 )^2 - 7# , and equate it to #0#
#x^2 - 4x - 3 = 0#
Solution by quadratic formula gives roots:
#( 2 + sqrt7 , 0 )# and #( 2 - sqrt(7) , 0 )#
#y# axis intercept is where #x = 0#
#y = (0)^2 - 4(0) -3 #
# ( 0 , -3 ) #
So all plotting points are:
#( 2 , -7 )# ,#( 2 + sqrt7 , 0 )# , #( 2 - sqrt(7) , 0 )# , # ( 0 , -3 ) #
Graph:
graph{x^2 -4x -3 [-5, 10, -12.8, 20]}
This can be viewed as the graph of #y = x^2# translated 2 units to the right and 7 units in the #- y # direction.
