Find Range of Quadratic Functions
Find the range of quadratic functions; examples and matched problems with their answers are located at the bottom of this page.
Graphical Analysis of Range of Quadratic FunctionsThe range of a function y = f(x) is the set of values y takes for all values of x within the domain of f.
The graph of any quadratic function, of the form f(x) = a x2 + b x + c, which can be written in vertex form as follows
Therefore if a > 0, the graph of f has a minimum point and if a < 0, the graph of f has a maximum point. Both minima or maxima are the vertices of the parabolas with coordinates (k , k) where h = - b / 2a and k = f(h).
Examples with Solutions
Example 1Find the range of function f defined by
Solution to Example 1
Matched Problem 1:Find the range of function f defined by
Example 2Find the range of function f defined by
Solution to Example 2
Matched Problem 2:Find the range of function f defined by
Answers for Matched Problems1) (-∞ , 3 ]
2) [ 6.5 , +∞ )
More References and linksFind domain and range of functions,
Find the range of functions,
find the domain of a function and mathematics tutorials and problems.