Asked Feb 21, 2019

Find the domain and range of f(x)= 3x^2-12x+2 .
Identify if it has a maximum or a minimum. Find the vertex of this parabola.


Expert Answer

Step 1

We have been given a quadratic function f(x) = 3x^2-12x+2. We are supposed to find its domain and range and the vertex.

Since the given function is a quadratic polynomial, its domain is all real numbers. For finding range of this function, we will have to find the vertex first. So, we will answer that part later on.

Since leading coefficient of the given quadratic function is positive, therefore, it will have a minimum.

Step 2

In order to find vertex of this quadratic function, we will use the formula x = -b/(2a) as shown below. And then we will substitute this value of x in the function to find the y coordinate of vertex, also shown below:

Step 3

From the vertex and the fact that it is an upward parabola, we can write the range of t...

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