# What is the axis of symmetry and vertex for the graph f(x) = 3 + 2x – x^2?

May 12, 2016

axis of symmetry is $x = 1$
Vertex is at $\left(1 , 4\right)$

#### Explanation:

This is an example of a parabola. It has the standard form:
$f \left(x\right) = y = a {x}^{2} + b x + c$
In $f \left(x\right) = - {x}^{2} + 2 x + 3 \text{ }$ a = -1, b = 2, c = 3.

The formula to find the axis of symmetry is: $x = \frac{- b}{2 a}$

$x = \frac{- 2}{2 \left(1\right)} = 1$

The vertex lies on the axis of symmetry, if $x = 1$

$y = - \left(1\right) + 2 \left(1\right) + 3 = 4$

Vertex is at (1,4)