Question 388348
1 Use the discriminant to determine whether the quadratic equation has two unequal real solutions, a repeated real solution, or no real solution without solving the equation. 
5x2 - 2x - 1 = 0
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b^2-4ac = 2^2-4*5*-1 > 0, so there are 2 unequal Real Number solutions. 

repeated real solution 
two unequal real solutions 
no real solution
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2 Write the general form of the equation of the circle with radius r and center (h, k). 
r = 2; (h, k) = (4, -4)
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(x-4)^2 + (y+4) = 2^2
x^2-8x+16 + y^2+8y+16 = 4
x^2 + y^2 -8x+8y + 28 = 0
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x2 + y2 + 8x - 8y + 20 = 0 
x2 + y2 + 8x + 8y + 20 = 0 
x2 + y2 - 8x - 8y + 20 = 0 
x2 + y2 - 8x + 8y + 20 = 0
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3 Write the standard form of the equation of the circle with radius r and center (h, k). 
r = 10; (h, k) = (4, -10)
(x-4)^2 + (y+10)^2 = 100
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(x + 4)2 + (y - 10)2 = 100 
(x + 4)2 + (y - 10)2 = 10 
(x - 4)2 + (y + 10)2 = 100 
(x - 4)2 + (y + 10)2 = 10
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Cheers,
Stan H.
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