Question

How do you find domain and range of a quadratic function?

Answer 1

Hint: Set of all possible outputs is called range whereas set of all possible inputs is called domain. There are three forms of the standard equation, the quadratic form of a quadratic equation looks like: $f(x) = {a^2} + bx + c$. So let us see how we can solve this problem.

Complete step by step solution:
We know that the domains of all quadratic functions are real numbers. We assume that both range and domain are real numbers to find domain and range of any function.
Since the domain is about inputs, we only observe how the graph looks horizontally.
For the range, we only observe how the graph looks vertically.
For a quadratic equation of vertex form, if a is positive, the function opens up and if a is negative, the functions open down. A vertex form looks like: $f(x) = a{(x - h)^2}$. The same goes for factored form and standard form.

Note:
In the above solution we have shown how we can find the range and domains of the quadratic function. Also, the domain of all the quadratic functions has a set of all real values for the domain. We have seen that the method of finding the domain and range for all the three forms of quadratic equations are the same.