How do you find the maximum value of  Y= -2(x+5)²-8?

Oct 17, 2016

The maximum value of the function is $- 8$.
$y = a {\left(x - h\right)}^{2} + k$, where $\left(h , k\right)$ is the vertex of the graph of the function. Also, if $a > 0$, the parabola will open upward and the $y$-coordinate of the vertex will be the minimum value of the curve. If $a < 0$, the parabola will open downward and the $y$-coordinate of the vertex will be the maximum value of the curve.
In $y = - 2 {\left(x + 5\right)}^{2} - 8$, $a = - 2$ and $- 2 < 0$, so the parabola will open downward and the maximum value of the curve will be the $y$-coordinate of the vertex, or $k$. In this equation, $k = - 8$, so the maximum valu of the function is $- 8$.