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-interecept (-3/2,0) and y-intercept (0,3). Find a and b.
The slope of the line is 2, so
y-a^2 = 2(x-a)
y = 2x+(a^2-2a)
2(-3/2) + a^2-a = 0
a^2-a-2 = 0
2(0) + b^2-b = 3
b^2-b-3 = 0
Now you can find a and b, and pick the ones that work with the line.