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Question Number 185014 by Mastermind last updated on 19/Jan/23
The relation y=x^2 +kx+c, where K  and C are constant passes through  the points (−1, −2) and (1, 8) in the  coordinate axes. calculate the value  of C and K.      M.m
$$\mathrm{The}\:\mathrm{relation}\:\mathrm{y}=\mathrm{x}^{\mathrm{2}} +\mathrm{kx}+\mathrm{c},\:\mathrm{where}\:\mathrm{K} \\ $$$$\mathrm{and}\:\mathrm{C}\:\mathrm{are}\:\mathrm{constant}\:\mathrm{passes}\:\mathrm{through} \\ $$$$\mathrm{the}\:\mathrm{points}\:\left(−\mathrm{1},\:−\mathrm{2}\right)\:\mathrm{and}\:\left(\mathrm{1},\:\mathrm{8}\right)\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{coordinate}\:\mathrm{axes}.\:\mathrm{calculate}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:\mathrm{C}\:\mathrm{and}\:\mathrm{K}. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$
Commented by Mastermind last updated on 19/Jan/23
It was a typo , it has been corrected
$$\mathrm{It}\:\mathrm{was}\:\mathrm{a}\:\mathrm{typo}\:,\:\mathrm{it}\:\mathrm{has}\:\mathrm{been}\:\mathrm{corrected} \\ $$
Answered by Rasheed.Sindhi last updated on 19/Jan/23
y=x^2 +kx+c  passes through (−1,−2):  −2=(−1)^2 +k(−1)+c          k−c=3...........(i)  passes through (1,8):  8=(1)^2 +k(1)+c          k+c=7..........(ii)  (i)+(ii):   2k=10⇒k=5  (ii):   5+c=7⇒c=2
$${y}={x}^{\mathrm{2}} +{kx}+{c} \\ $$$${passes}\:{through}\:\left(−\mathrm{1},−\mathrm{2}\right): \\ $$$$−\mathrm{2}=\left(−\mathrm{1}\right)^{\mathrm{2}} +{k}\left(−\mathrm{1}\right)+{c} \\ $$$$\:\:\:\:\:\:\:\:{k}−{c}=\mathrm{3}………..\left({i}\right) \\ $$$${passes}\:{through}\:\left(\mathrm{1},\mathrm{8}\right): \\ $$$$\mathrm{8}=\left(\mathrm{1}\right)^{\mathrm{2}} +{k}\left(\mathrm{1}\right)+{c} \\ $$$$\:\:\:\:\:\:\:\:{k}+{c}=\mathrm{7}……….\left({ii}\right) \\ $$$$\left({i}\right)+\left({ii}\right):\:\:\:\mathrm{2}{k}=\mathrm{10}\Rightarrow{k}=\mathrm{5} \\ $$$$\left({ii}\right):\:\:\:\mathrm{5}+{c}=\mathrm{7}\Rightarrow{c}=\mathrm{2} \\ $$

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