# How do you find the axis of symmetry, graph and find the maximum or minimum value of the function y=-2x^2-1?

Mar 24, 2016

Axis of symmetry is the y-axis

Maximum ->(x,y) = (0,-1) )

#### Explanation:

Consider the standard form of $y = a {x}^{2} + b x + c$

We are given $y = - 2 {x}^{2} - 1$

Observe that there is no $b x$ term implying that the axis if symmetry is at $x = 0$. Thus the axis of symmetry is the y-axis.

Observe that the coefficient of ${x}^{2}$ is negative . This means that the general shape of the graph is $\cap$ so we have a maximum.

The constant of -1 is the y-intercept so the maximum is $\left(x , y\right) \to \left(0 , - 1\right)$