for the quadratic function, y=(x-6)^2 + 11.
a) identify the transformations from the graph of y=x^2
b)state the domain and range of y=(x-6)^2 + 11
c)write an equation for the graph
a) The transformations from the graph of y=x^2 to y=(x-6)^2 + 11 are:
1) Translation 6 units to the right: The entire graph has been shifted 6 units to the right from the original graph y=x^2.
2) Translation 11 units up: The entire graph has been shifted 11 units up from the original graph y=x^2.
b) The domain of y=(x-6)^2 + 11 is all real numbers, as there are no restrictions on the possible input values of x.
The range of y=(x-6)^2 + 11 is y ≥ 11, meaning that the minimum value of y is 11, and there are no upper bounds on the possible output values of y.
c) The equation for the graph y=(x-6)^2 + 11 is y=x^2 translated 6 units to the right and 11 units up.