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

##### 1 Answer
Feb 3, 2016

The function has a maximum at $x = - 1$

Axis of symmetry is -

$x = - 1$

#### Explanation:

Given -

$y = - {x}^{2} + 2 x + 1$

$\frac{\mathrm{dy}}{\mathrm{dx}} = - 2 x + 2$
$\frac{{d}^{2} y}{{\mathrm{dx}}^{2}} = - 2$
$\frac{\mathrm{dy}}{\mathrm{dx}} = 0 \implies - 2 x + 2 = 0$

$x = \frac{2}{- 2} = - 1$

At $x = - 1$; $\frac{\mathrm{dy}}{\mathrm{dx}} = 0$;>$\frac{{d}^{2} y}{{\mathrm{dx}}^{2}} < 0$

Hence the function has a maximum at $x = - 1$

Axis of symmetry is -

$x = - 1$