Question

Move the sliders h and k so that the graph of y = x2 gets shifted up 2 units and to the right 3 units. Then type the new function, f(x) in the answer box 4 3 2 1 -3 -2 - 1 0 1 2 3 f(2) -1 h = 0.00 -2 k = 0.00 O + → Don't forget to shift the graph. Using function notation, i.e. f(x) = , enter the function that results from the transformation.

Answer 1

Shifting the graph of y = x^2 up 2 units and to the right 3 units yields the function f(x) = (x + 3)^2 + 2, and f(2) = 27 after the transformation.

To shift the graph of y = x^2 up 2 units and to the right 3 units, we apply vertical and horizontal translations. The general form for such transformations is f(x) = (x - h)^2 + k, where h is the horizontal shift, and k is the vertical shift.

For the given shift up 2 units, we use k = 2, and for the shift to the right 3 units, we use h = -3 (since the shift is in the opposite direction).

Applying these values, the new function is f(x) = (x - (-3))^2 + 2, which simplifies to f(x) = (x + 3)^2 + 2.

Now, if we evaluate f(2), we substitute x = 2 into the new function: f(2) = (2 + 3)^2 + 2 = 5^2 + 2 = 27.

Therefore, the resulting function from the specified transformations is f(x) = (x + 3)^2 + 2, and f(2) = 27 after the shift.

Answer 2

h is the horizontal translation.

k is the vertical translation.

• h should be moved 3 units to shift the graph

,

• k should be moved 2 units to shift the graph

Some translation rules