Consider the parabolas y=x^2 and y=a(x-b)^2+c, where a,b,c are all real numbers (a) Derive an equation...

Consider the parabolas y=x^2 and y=a(x-b)^2+c, where a,b,c are all real numbers

(a) Derive an equation for a line tangent to both of these parabolas (show all steps with a proof, assuming that such a line exists)

(b) Assume that the doubly-tangent line has an equation y+Ax+B. Find an example of values of a,b,c (other than the ones given here) such that A,B ∈ Z

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Colby Messinger answered 2 years ago

Consider the parabolas y=x^2 and y=a(x-b)^2+c, where a,b,c are all real numbers (a) Derive an equation...

Consider the parabolas y=x^2 and y=a(x-b)^2+c, where a,b,c are all real numbers (a) Derive an equation for a line tangent to both of these parabolas (show all steps, assuming that such a line exists) (b) Assume that the doubly-tangent line has an equation y+Ax+B. Find an example of values of a,b,c (other than the ones given here or in class) such that A,B ∈ Z (c) Consider the case a = 1. Does your algebra accurately reflect what we can...

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Consider the parabolas y=x^2 and y=a(x-b)^2+c, where a,b,c are all real numbers (a) Derive an equation...

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