Question

Pedro knows that y=x2

is the parent graph of a quadratic. What steps should he take if he wants to transform the parent graph to obtain the graph of y=(x−7)2+3
?

Answer 1

To transform the parent graph y = x^2 into the graph of y = (x - 7)^2 + 3, Pedro can follow these steps:

1. Horizontal Translation: To shift the graph horizontally, he needs to subtract the desired amount from the x-values. In this case, he wants to shift the graph 7 units to the right, so he can replace 'x' with '(x - 7)'.

y = (x - 7)^2

2. Vertical Translation: To shift the graph vertically, he needs to add the desired amount to the y-values. In this case, he wants to shift the graph 3 units upward, so he can add '+ 3' at the end of the equation.

y = (x - 7)^2 + 3

By following these steps, Pedro can transform the parent graph y = x^2 into the desired graph y = (x - 7)^2 + 3, which represents a horizontal shift to the right by 7 units and a vertical shift upward by 3 units.