Describe the transformation from the parent graph of y - 4 = – 2(x – 3)^2. Graph
both the parent graph and the transformed graph on the grid provided. Plot at least
three distinct points for each.
we have that
the parent function is
y=x^2
Is a vertical parabola open upward with the vertex at (0,0)
the transformed function
is
y-4=-2(x-3)^2
y=-2(x-3)^2+4
Is a vertical parabola open downward with vertex at (3,4)
so
The transformations are
1) Reflection over x-axis
Rule is
(x,y) ------> (x,-y)
y=x^2 ------------------> y=-x^2
2) Vertical Dilation with a scale factor of 2
Rule
(x,y) --------> (x,2y)
y=-x^2 ----------> y=-2x^2
3) Translation 3 units at right and 4 units up
Rule is
(x,y) --------> (x+3,y+4)
y=-2x^2 --------> y=-2(x-3)^2+4
see the graph to better understand the problem