Question

function g is a transformation of the parent function f(x)=x^2 the graph of g is a translation right 2 and down 5units of the graph of f what is the equation of function g written in the form y=ax^2+bx+c?

Answer 1

right 3 units down 5 units

$f(x)=x^2$

right 3 units = (3,0)

down 5 units = (0,-5)

vertex = (h,k) therefore.

$g(x)=(x-3)^2-5$

Then convert the vertex form into standard form for the equation in the choice.

$g(x)=(x-3)^2-5\\g(x)=(x^2-6x+9)-5+9\\g(x)=(x^2-6x)+4\\g(x)=x^2-6x+4$

Thus, the answer is B.