Question 468430
f(x) = -2x^2 - 5x + 1
:
-2x^2 - 5x + ___ = -1
divide by -2, change the signs
x^2 + {{{5/2}}}x + ___ = {{{1/2}}}
:
Find the term that will complete the square, add to both sides
Divide the coefficient of x by 2 and square it (5/4)^2 = 25/16
x^2 + {{{5/2}}}x + {{{25/16}}} = {{{1/2}}} + {{{25/16}}}
:
x^2 + {{{5/2}}}x + {{{25/16}}} = {{{8/16}}} + {{{25/16}}}
:
x^2 + {{{5/2}}}x + {{{25/16}}} = {{{33/16}}}
:
(x + {{{5/4}}})^2 = {{{33/16}}}
:
x + {{{5/4}}} = +/- {{{sqrt(33/16)}}}
Two solutions
x = {{{-5/4}}} + {{{1/4}}}{{{sqrt(33)}}}
x = {{{(-5 + sqrt(33))/4}}}
and
x = {{{-5/4}}} - {{{1/4}}}{{{sqrt(33)}}}
x = {{{(-5 - sqrt(33))/4}}}
:
:
The graph
{{{ graph( 300, 200, -6, 5, -10, 10, -2x^2-5x+1) }}}