How do you find domain and range for # f(x) = (x^2) - 2x - 15#?

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Answer 1 · 2015-10-02T15:53:01

This is an equation of a parabola that opens upward and will have a minimum value for y at the vertex.

Since this is a parabola opening upward, the domain is all real values for x: #(-oo,oo)#

The general formula for a parabola is:

#f(x)=ax^2+bx+c#

Now, find the vertex using this formula for the x-coordinate:

#x=-b/(2a)# = #-(-2)/(2*1)# = #1#

Finally, we can find the lower limit for y by inserting the x-coordinate of the vertex into the original equation:

#f(1)=(1^2)-(2)(1)-15=-16#

So, the range is #[-16, oo)#

Here is a graph of the parabola:

enter image source here

hope that helped