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# Coordinates

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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 unqiue line that contains the point A and the point B) has x-intercept (-3/2,0) and y-intercept (0,1).  Find a and b.  Express your answer as the ordered pair (a,b).

Dec 29, 2021

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Hello Guest!

$$f(x)=\frac{1}{1.5}x+1\\ g(x)=x^2\\ f(x)=g(x)$$

$$\frac{2}{3}\cdot x+1=x^2\\ x^2-\frac{2}{3} x-1=0\\ x=\frac{1}{3}\pm \sqrt{\frac{1}{9}+1}$$

$$x\in \{-0.721,1.387\}$$

$$\{a,b\}=\{-0.721,1.387\}$$

!

Dec 29, 2021