# How do you find the domain and range of Y=-x^2+4x-1?

May 28, 2017

See explanation.

#### Explanation:

The function is a polynomial, so it is defined for all real values of $x$. This means that the domian is $D = \mathbb{R}$

To calculate the range we have to find the vertex of the parabola:

$p = \frac{- b}{2 a} = \frac{- 4}{-} 2 = 2$

$q = f \left(p\right) = - {2}^{2} + 4 \cdot 2 - 1 = 3$
graph{-x^2+4x-1 [-11.25, 11.25, -5.625, 5.625]}

From the graph we see that the range is (-oo;3]