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

Oct 2, 2015

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

#### Explanation:

Since this is a parabola opening upward, the domain is all real values for x: $\left(- \infty , \infty\right)$

The general formula for a parabola is:

$f \left(x\right) = a {x}^{2} + b x + c$

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

$x = - \frac{b}{2 a}$ = $- \frac{- 2}{2 \cdot 1}$ = $1$

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

$f \left(1\right) = \left({1}^{2}\right) - \left(2\right) \left(1\right) - 15 = - 16$

So, the range is $\left[- 16 , \infty\right)$

Here is a graph of the parabola:

hope that helped