find a quadratic function of the form f(x)=ax^2+by+c that satisfies the given conditions. The graph of f is obtained by shifting the graph of y=x^2+2x+2 three

Question

units horizontally to the right and two units vertically down. 

Answer 1

First, get y in vertex form.

 

y = (x² + 2x + 1) + 2 - 1

 

y = (x + 1)² + 1

 

Vertex is (-1, 1).

 

New vertex is (-1 + 3 , 1 - 2) = (2, -1)

 

f(x) = (x - 2)² - 1

f(x) = x² - 4x + 3