# What is the axis of symmetry and vertex for the graph y=-x^2+4x+1?

Oct 26, 2017

axis of symmetry: $x = 2$
vertex: $\left(2 , 5\right)$

#### Explanation:

convert $- {x}^{2} + 4 x + 1$ into $p {\left(x + q\right)}^{2} + r$ form:

$- {x}^{2} + 4 x + 1 = - \left({x}^{2} - 4 x - 1\right)$

${x}^{2} - 4 x - 1 = \left({x}^{2} - 4 x + 4\right) - 5$

$= {\left(x - 2\right)}^{2} - 5$

$- \left({x}^{2} - 4 x - 1\right) = - \left({\left(x - 2\right)}^{2} - 5\right) = - {\left(x - 2\right)}^{2} + 5$

$p {\left(x + q\right)}^{2} + r = - {\left(x - 2\right)}^{2} + 5$

$p = 1 , q = - 2 , r = 5$

axis of symmetry: $x = - q$

here, $x = 2$

coordinates of vertex: $\left(- q , r\right)$

here, this is $\left(2 , 5\right)$