Given the parent function:
first, to translate it 1 unit right, we have to find f(x-1):
next, to translate it 2 units down, we have to find the following expression:
combining both transformations, we get:
therefore, g(x) = e^(x-1) - 2 is the translation of the parent function 1 unit right and 2 units down
The specified function's vertex form is
If a quadratic equation is written in the form
then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)
<h3>What is a perfect square polynomial?</h3>If a polynomial p(x) can be written as:
where f(x) is also a polynomial, then p(x) is called as perfect square polynomial
For the considered case, the polynomial specified is;
Thus, the vertex form of the considered polynomial is
Standard form of a quadratic polynomial is
Thus, we get: the considered polynomial in standard form as:
The considered polynomial has only two terms, therefore, its not a trinomial.
Thus, the specified function's vertex form is
Learn more about vertex form of a quadratic equation here: