Question

Sansa shifted the parabola y = x^2 by 3 units to the right. Which of the following equations corresponds to the resulting graph?

А) y = x2 + 3
B) y = x2 + 9
C) y = x2 + 6x + 9
D)y = x2 - 6x + 9

Answer 1

y = (x - 3)^2

Explanation:

The original function is y = x^2. Its vertex is at (0, 0). Translating the graph h units to the right results in g(x) = (x - h)^2; h units to the left results in h(x) = (x + h)^2.

In this particular case we have y = x^2 and are translating the graph 3 units to the right. Thus, the original function y = x^2 becomes y = (x - 3)^2.