Question

The parent function of a quadratic, f(x) = x², is translated 9 units right and 4 units up. Write the equation of the transformed quadratic function, g(x), in vertex form.

Answer 1

The transformed quadratic function g(x), after being translated 9 units to the right and 4 units up from the parent function f(x) = x², is g(x) = (x-9)² + 4.

Step-by-step explanation:

The student has asked to write the equation of a transformed quadratic function g(x) when the parent function f(x) = x² is translated 9 units to the right and 4 units up. The translation of a function can be represented in its vertex form, which for a quadratic function is g(x) = a(x-h)² + k, where (h, k) is the vertex of the parabola.

In this case, since the transformation is 9 units right and 4 units up, we can denote the new vertex as (9, 4). Therefore, the equation in vertex form is:

g(x) = (x-9)² + 4.

This represents the equation of the quadratic function after it has undergone the given translations.