# How do you find the domain and range of g(x)=-x^2-3x-1?

Mar 31, 2017

Domain: $x \in \mathbb{R}$ . Range: $g \left(x\right) \le 1.25$

#### Explanation:

$g \left(x\right) = - {x}^{2} - 3 x - 1 , a = - 1 , b = - 3 , c = - 1$
Domain (possible value of x): Any real value i.e $x \in \mathbb{R}$

Range: This is an equation of parabola , opening downwards, since $a$ is negative.
Vertex(x) $= - \frac{b}{2 a} = \frac{3}{-} 2 = - 1.5$
Vertex(y) $g \left(x\right) = - {\left(- 1.5\right)}^{2} - 3 \cdot \left(- 1.5\right) - 1 = 1.25$

Vertex is at $\left(- 1.5 , 1.25\right) \therefore 1.25$ is the maximum point.
Therefore Range, $g \left(x\right) \le 1.25$ graph{-x^2-3x-1 [-10, 10, -5, 5]} [Ans]