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

Jun 4, 2017

Line of symmetry is $x = 1$ and the maximum value is at $\left(1 , 4\right)$

#### Explanation:

$y = a {x}^{2} + b x + c$ is the standard form of the equation of a parabola.

You can find the line of symmetry by using the formula:

$x = \frac{- b}{2 a}$

So, for $y = - {x}^{2} + 2 x + 3 \text{ } x = \frac{- 2}{2 \left(- 1\right)}$

$x = 1$

This also gives you the $x$-co-ordinate of the vertex.
Substitute $x = 1$ to find $y$

$y = - {\left(1\right)}^{2} + 2 \left(1\right) + 3 \text{ } \rightarrow y = 4$

We see that $a < 0$, which means that the graph has a maximum turning point with the arms open downwards.

The point $\left(1 , 4\right)$ is the maximum value for the function.