Question

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

Answer 1

`x=0` & `y_{max}=-3`

Explanation:

Given equation of curve: `y=-2x^2-3`

`x^2=-\1/2(y+3)`

Above equation is in standard form of downward parabola `X^2=-4AY` with axis of symmetry `X=0`

hence, `x=0` i.e. y-axis is the axis of symmetry of given parabola: `y=-2x^2-3`

Now, differentiating given equation w.r.t. `x` as follows

`\frac{dy}{dx}=-4x`
`\frac{dy}{dx}=0\implies -4x=0\ or \ x=0`

`\frac{d^2y}{dx^2}=-4<0`

hence, the given function: `y=-2x^2-3` has maxima at `x=0` & maximum value is given as

`y_{max}=-2(0)^2-3=-3`