Question 937243
Use completing the square to describe the graph of the following function. Support your answer graphically 
:
{{{ f(x)=-2x^2+4x+5 }}}
-2x^2 + 4x + 5 = 0
coefficient of x^2 has to be 1, divide equation by -2
x^2 - 2x - 2.5 = 0
x^2 - 2x + ___ = 2.5
Complete the square, divide the coefficient of x by 2 and square it
add it to both sides
x^2 - 2x + 1 = 2.5 + 1
x^2 - 2x + 1 = 3.5
which is
(x-1)^2 = 3.5
find the square root of both sides
x - 1 = +/-{{{sqrt(3.5)}}}
Two solutions
x = 1 + {{{sqrt(3.5)}}} approx 2.87
and
x = 1 - {{{sqrt(1.5)}}} approx -.87
:
Graph the original equation, check the x intercepts
{{{ graph( 300, 200, -2, 5, -10, 10, -2x^2+4x+5) }}}