Question

Use the following description to write the quadratic function, g(x), in vertex form: The parent function f(x) = x^2 has a vertical stretch of 2 and is translated 7 units left and 3 units down.

Answer 1

The quadratic function g(x) in vertex form, after applying the given transformations to the parent function, is g(x) = 2(x - 7)^2 - 3.

Step-by-step explanation:

The student is asking to write the quadratic function g(x) in vertex form based on the given transformations of a parent function f(x) = x2.

Since there is a vertical stretch by a factor of 2, the coefficient a in the vertex form y = a(x - h)2 + k will be 2. The translation 7 units to the left will determine h as +7, and the translation 3 units down will make k -3. Therefore, the vertex form of the quadratic function is g(x) = 2(x - 7)2 - 3.