# How do you find the axis of symmetry, and the maximum or minimum value of the function y = -x^2 - 3x -5?

Oct 24, 2017

Axis of symmetry is $x = - 1.5$, maximum value is $- 2.75$
and minimum value extends to $- \infty$.

#### Explanation:

$y = - {x}^{2} - 3 x - 5 \mathmr{and} y = - \left({x}^{2} + 3 x\right) - 5$ or

$y = - \left({x}^{2} + 3 x + {1.5}^{2}\right) + 2.25 - 5$ or

$y = - {\left({x}^{2} + 1.5\right)}^{2} - 2.75$ . This is vertex form of

equation y=a(x-h)^2+k ; a=-1 ,h=-1.5 ,k=-2.75

Therefore vetex is at $\left(h , k\right) \mathmr{and} \left(- 1.5 , - 2.75\right)$

Axis of symmetry is x= h or x =-1.5 ; a is negative,

so parabola opens downward. Therefore vertex is the

maximum point $\left(- 1.5 , - 2.75\right) \therefore$ Maximum value is $- 2.75$

and minimum value extends to $- \infty$.

graph{-x^2-3x-5 [-20, 20, -10, 10]} [Ans]