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

##### 1 Answer

$x = 0$ & ${y}_{\max} = - 3$

#### Explanation:

Given equation of curve: $y = - 2 {x}^{2} - 3$

${x}^{2} = - \setminus \frac{1}{2} \left(y + 3\right)$

Above equation is in standard form of downward parabola ${X}^{2} = - 4 A Y$ with axis of symmetry $X = 0$

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

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

$\setminus \frac{\mathrm{dy}}{\mathrm{dx}} = - 4 x$
$\setminus \frac{\mathrm{dy}}{\mathrm{dx}} = 0 \setminus \implies - 4 x = 0 \setminus \mathmr{and} \setminus x = 0$

$\setminus \frac{{d}^{2} y}{{\mathrm{dx}}^{2}} = - 4 < 0$

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

${y}_{\max} = - 2 {\left(0\right)}^{2} - 3 = - 3$