Question 676328
find the x intercepts, there will be two as indicated by {{{x^2}}}
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{{{-(x^2-2x-1) = 0}}}
Use quadratic equation
{{{x = (-(-2)+-sqrt((-2)^2-4(1)(-1)))/((2)(1)))}}}
{{{x = (2 +- sqrt(4--4))/(2)}}}
{{{x = (2 +- sqrt(8))/2}}}
{{{x = (2 +- 2sqrt(2))/2}}}
{{{x = 1 +- sqrt(2)}}}
x = 1 + {{{sqrt(2)}}} = 2.4
x = 1 - {{{sqrt(2)}}} = -.4
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Choose a couple of values for x and solve for y
x: {{{-x^2+2x+1}}}: (x,y)
3: -(3^2) + 2(3) + 1 = -9+6+1 = -2: Plot (3,-2)
2: -(2^2) + 2(2) + 1 = -4+4+1 = 1: Plot (2,1)
1: -(1^2) + 2(1) + 1 = -1+2+1 = 2: Plot (1,2)
0: -(0^2) + 2(0) + 1 = 0+0+1 = 1: Plot (0,1)
-1: -(-1^2) + 2(-1) +1 = -1-2+1 = -2: Plot (-1,-2)
-2: -(-2^2) + 2(-2) +1 = -4-4+1 = 1: Plot (-2,1)
-3: -(-3^2) + 2(-3) +1 = -9-6+1 = -14: Plot (-3,-14)
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{{{graph(300,200,-5,10,-20,5,-x^2+2x+1)}}}
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