Describe the transformation of parent function f(x) = x^2

Question

Describe the transformation of parent function f(x) = x^2

g(x) -(x + 5)^2 + 2

Answer 1

When you add a constant to a function (in this case +2), the curve for the parent function is moved up 2 units. When you add a constant to the variable of the function (+5), the curve is translated 5 units to the left ( a + constant moves the curve to the left, and a negative constant moves it to the right), A negative sign in front of the function reflects the curve along the x axis (the reflected curve is the mirror image along the x axis).

The combination of all 3 operations ends up with a curve shifted 2 units up, 5 units to the left, and a reflection along the x axis).

The parent curve is a parabola opening in the y direction with the vertex at the origin. The transformed curve is a down opening parabola with the vertex at (-5,-2).