How do you find domain and range of a quadratic function?
2 Answers
The domain is all real numbers and the range is all the reals at or above the vertex y coordinate (if the coefficient on the squared term is positive) or all the reals at or below the vertex (if said coefficient is negative).
See explanation...
Explanation:
Suppose:
#f(x) = ax^2+bx+c \ # where#a != 0#
First note that
We can complete the square and find:
#f(x) = a(x+b/(2a))^2+c-b^2/(4a)#
This is vertex form for a parabola with vertex at
Note that for real values of
#(x+b/(2a))^2 >= 0#
with equality when
Hence if
In fact for any
#f((-b+-sqrt(b^2-4a(c-y)))/(2a)) = y#
So the range of
Similarly if
#f((-b+-sqrt(b^2-4a(c-y)))/(2a)) = y#
So the range of