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\(\text{A parabola with equation $y=x^2+bx+c$ passes through the points $(2,3)$ and $(4,3)$. What is $c$? }\)

 Aug 15, 2019
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\(\text{just plug the points in and solve the resulting equations}\\ 2^2 + b(2) + c = 3\\ 4^2 + b(4) + c = 3\\~\\ 4 + 2b + c = 3\\ 16+4b+c = 3\\ \text{subtract twice (1) from (2)}\\ 8-c=-3\\ c=11\)

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 Aug 15, 2019

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