Question 97832
<pre><b>
what is the equation of the line of symmetry for y = -x² + 4x + 5

The vertex for the quadratic equation:

y = ax² + bx + c

is given by the formula:

({{{-b/(2a)}}}, {{{-D/(4a)}}}), where D = discriminant = {{{b^2-4ac}}}

and the line of symmetry is the vertical line
whose equation is 

x = {{{-b/(2a)}}}

==============================

For the quadratic equation:

y = -x² + 4x + 5

a = -1, b = 4, c = 5

D = discriminant = {{{b^2-4ac}}} = {{{4^2-4*-1*5}}} = {{{16+20}}} = {{{36}}}

So the vertex is

({{{-b/(2a)}}}, {{{-D/(4a)}}}) = ({{{-4/(2*-1)}}}, {{{-36/(4*-1)}}}) = 
({{{-4/(-2)}}}, {{{-36/(-4)}}}) = ({{{2}}}, {{{9}}}),    

and the line of symmetry is the vertical line
whose equation is 

x = {{{-b/(2a)}}}

or

x = 2

Here is the graph of the quadratic and the
green vertical line is the line of symmetry,
notice it crosses the x axis at 2.

{{{graph(222.2222222,375,-3,7,-8,10, -x^2+4x+5,999(x-2))}}}

Edwin</pre>