# How do you find the range of #f(x)=abs(x^2-8x+7)# for the domain #3 <= x <= 8#?

##### 1 Answer

There are several approaches that will work quite well for this. Here's the one that I used:

Graph the parabola

I chose this method, because it's relatively easy to find the

The vertex has

graph{y = x^2-8x+7 [-18.32, 27.29, -11.85, 10.94]}

No graph the absolute values:

graph{y =abs( x^2-8x+7) [-7.87, 20.61, -1.88, 12.35]}

Now:

The maximum value of the absolute value on that domain will be the absolute value of the minimum of the parabola or

The range for that domain is