SOLUTION: use the completing the square to describe the graph of the following function support your answer graphically
{{{ f(x)=-x^2+2x+5 }}}
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-> SOLUTION: use the completing the square to describe the graph of the following function support your answer graphically
{{{ f(x)=-x^2+2x+5 }}}
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Question 937256: use the completing the square to describe the graph of the following function support your answer graphically
Found 2 solutions by ewatrrr, TimothyLamb:Answer by ewatrrr(24785) (Show Source):
You can put this solution on YOUR website! -x^2 + 2x + 5 = 0
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the above quadratic equation is in standard form, with a=-1, b=2 and c=5
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
-1 2 5
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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the quadratic has two real roots (y = 0) at:
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x = -1.44948974
x = 3.44948974
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the quadratic has a vertex (maximum) at: ( 1, 6 )
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the quadratic is a parabola that opens downward
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now, by completing the square:
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general quadratic:
ax^2 + bx + c = 0
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divide both sides by a:
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(-x^2 + 2x + 5 = 0)/-1
x^2 - 2x - 5 = 0
x^2 - 2x = 5
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complete the square:
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x^2 - 2x + (-2/2)^2 - (-2/2)^2 = 5
x^2 - 2x + (-1)^2 - (-1)^2 = 5
x^2 - 2x + (-1)^2 - 1 = 5
(x - 1)^2 = 6
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solve for x:
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sqrt( (x - 1)^2 ) = sqrt( 6 )
x - 1 = sqrt( 6 )
x = 1 (+ or -) sqrt( 6 )
x = 1 + sqrt( 6 )
x = 3.44948974278
x = 1 - sqrt( 6 )
x = -1.44948974278
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