Minimize Distance from Point to Parabola (Optimization) | Calculus 1 Exercises

[@williamvasquez4857]

Why is 4 minus the negative square root = to 4 minus the positive square root in your very last equation?

[@WrathofMath]

Thanks for watching! I'm not 100% sure what you're describing, I see when x=-sqrt(3/2) in the second to last equation we have y = 4 - (-sqrt(3/2))^2. Since (-sqrt(3/2)) is being squared, the negative goes away and so too does the square root.

[@williamvasquez4857]

So basically -sqrt(x) is the same as +sqrt(x).

[@WrathofMath]

@@williamvasquez4857 No, (-sqrt(x))^2 is the same as sqrt(x)^2. Squaring the negative makes it positive, so if a negative quantity is being squared, the negative can be disregarded.