SOLUTION: Let a and b be real numbers, where a < b, and let A = (a,a^2) and B = (b,b^2). The line AB (meaning the unique line that contains the point A and the point B) has x-intercept (-3/2

Algebra ->  Graphs -> SOLUTION: Let a and b be real numbers, where a < b, and let A = (a,a^2) and B = (b,b^2). The line AB (meaning the unique line that contains the point A and the point B) has x-intercept (-3/2      Log On


   

Question 1090934: Let a and b be real numbers, where a < b, and let A = (a,a^2) and B = (b,b^2). The line AB (meaning the unique line that contains the point A and the point B) has x-intercept (-3/2,0) and y-intercept (0,3). Find a and b. Express your answer as the ordered pair (a,b).
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
system%28y=mx%2B3%2Cm=%283-0%29%2F%280-%28-3%2F2%29%29=3%2F%283%2F2%29=2%29

highlight_green%28y=2x%2B3%29
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system%28%28b%5E2-a%5E2%29%2F%28b-a%29=2%2C%28a%5E2-3%29%2F%28a-0%29=2%29
b%5E2-a%5E2=2b-2a
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a%5E2-3=2a
a%5E2=2a%2B3
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b%5E2-2a-3=2b-2a
b%5E2-3=2b
b%5E2-2b-3=0
%28b%2B1%29%28b-3%29=0
system%28b=-1%2Cor%2Cb=3%29

If b=3, then B is (3,9)
and b%5E2-a%5E2=2b-2a becomes 9-a%5E2=6-2a
3-a%5E2=-2a
3%2B2a=a%5E2
a%5E2-2a-3=0
%28a-3%29%28a%2B1%29=0
Since b=3 is tried already, a=-1. A is (-1,1).

Check slope for (-1,1) & (3,9).
%289-1%29%2F%283-%28-1%29%29
8%2F4
highlight_green%282%29 as expected.


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Possible Solution: system%28a=-1%2Cb=3%29.
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FIT WITH EQUATION y=2x+3 ?
A (-1,1)
1=2%28-1%29%2B3
1=-2%2B3
1=1
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B+%283%2C9%29
9=2%2A3%2B3
9=6%2B3
9=9
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Yes.
(a,b) is (-1,3).