Domain Of A Quadratic Function

I want to go over this particular example because the minimum or maximum is not quite obvious.

Domain of a quadratic function. Determine the domain and range of the function f of x is equal to 3x squared plus 6x minus 2. What is a set of all of the valid inputs or all of the valid x values for this function. Therefore the domain of the given quadratic function is all real values. Comparing the given quadratic function y x 2 5x 6 with y ax 2 bx c.

Because in the above quadratic function y is defined for all real values of x. From algebra we know that polynomials including the quadratic function presented on statement are continuous in every part of real number set which means the existence of images for every element of domain. Domain of a quadratic function. The domain of any quadratic function in the above form is all real values.

The graph of this function is shown below. Therefore the domain of the quadratic function in the form y ax2 bx c is all real values. So the domain of the function is. The general form a quadratic function is.

The range of a function is the set of all real values of y that you can get by plugging real numbers into x. The domain of a function is the set of all real values of x that will give real values for y. And i can take any real number square it multiply it by 3 then add 6 times that real number and then subtract 2 from it. In the quadratic function y x 2 5x 6 we can plug any real value for x.

Because y is defined for all real values of x. Notice though that the parabola is in the standard form y ax 2 bx c. Domain of a parabola or domain of a quadratic function would just be the set of values for which the function exists and is valid. The quadratic parent function is y x2.

Just like our previous examples a quadratic function will always have a domain of all x values. Hence the domain of the quadratic function is all real numbers. That is domain x x r range.