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explicitvogue
 one year ago
Fan&medal to best help! What is the equation, in standard form, of a parabola that contains the following points?
(2,18), (0,2), (4,42)
A. y=2x^22x3
B. y=3x^2+2x2
C. y=3x^22x+2
D. y=2x^2+3x+2
explicitvogue
 one year ago
Fan&medal to best help! What is the equation, in standard form, of a parabola that contains the following points? (2,18), (0,2), (4,42) A. y=2x^22x3 B. y=3x^2+2x2 C. y=3x^22x+2 D. y=2x^2+3x+2

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0By the points you've given the parabola would be opening down so your quadratic would definitely be negative.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It actually opens up so its positive, oops I'll check my graphing calculator

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.0Using $$ (2,18), (0,2), (4,42) $$ We can solve $$ y=ax^2+bx+c $$ for a, b and c. Using (2,18), x=2 and y=18: $$ 18=a2^2+b(2)+c=4a2b+c $$ Using (0,2), x=0 and y=2: $$ 2=a0^2+b(0) + c=c $$ So now we know, c=2. Finally, for (4,42), x=4 and y=42: $$ 42=a4^2+b(4)+c=16a+4b+c $$ Putting this all together: $$ 18=4a2b+2\\ 42=16a+4b+2 $$ Adding 2 times the 1st equation to the second we get: $$ 2(18)=2(4a2b+2)\\ +\\ 42=16a+4b+2\\ =\\ 36+42=8a+16a4b+4b+4+2\\ 78=24a+6\\ 24a=786=72\\ a=72/24=3 $$ So, $$ 18=4(3)2b+2\\ 2b=1218+2=4\\ b=2 $$ We have found that a=3,b=2 and c=2: $$ y=3x^22x+2 $$ dw:1444452119003:dw Make sense?
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