Question

Write a quadratic function in vertex form that represents the given transformation and parent function f(x)=x^2. Vertical compression of 1/3 reflection across the X axis translation left eight units

Answer 1

Answer:

$g(x) = - \frac{1}{3} (x + 8)^{2}$

Step-by-step explanation:

The given parent function is

$f(x) = {x}^{2}$

We want to write a quadratic function in vertex form that is a result of transforming f(x) by a vertical compression of ⅓, reflection across the x-axis , and a translation 8 units left.

Let g(x) be the transformed function, then we have;

$g(x) = - \frac{1}{3} f(x + 8)$

The negative indicate a reflection in the x-axis, +8 indicates a shift to the left, and ⅓ is the vertical compression factor.

$g(x) = - \frac{1}{3} (x + 8)^{2}$