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Question Number 185014 by Mastermind last updated on 19/Jan/23

$$\mathrm{The}\mathrm{relation}\mathrm{y}={\mathrm{x}}^2+\mathrm{kx}+\mathrm{c},\mathrm{where}\mathrm{K}$$$$\mathrm{and}\mathrm{C}\mathrm{are}\mathrm{constant}\mathrm{passes}\mathrm{through}$$$$\mathrm{the}\mathrm{points}(-1,-2)\mathrm{and}(1,8)\mathrm{in}\mathrm{the}$$$$\mathrm{coordinate}\mathrm{axes}.\mathrm{calculate}\mathrm{the}\mathrm{value}$$$$\mathrm{of}\mathrm{C}\mathrm{and}\mathrm{K}.$$$$$$$$$$$$\mathrm{M}.\mathrm{m}$$

Commented by Mastermind last updated on 19/Jan/23

$$\mathrm{It}\mathrm{was}\mathrm{a}\mathrm{typo},\mathrm{it}\mathrm{has}\mathrm{been}\mathrm{corrected}$$

Answered by Rasheed.Sindhi last updated on 19/Jan/23

$$y=x^2+kx+c$$$$passesthrough(-1,-2):$$$$-2={(-1)}^2+k(-1)+c$$$$k-c=3...........\left(i\right)$$$$passesthrough(1,8):$$$$8={\left(1\right)}^2+k\left(1\right)+c$$$$k+c=7..........\left(ii\right)$$$$\left(i\right)+\left(ii\right):2k=10\Rightarrow k=5$$$$\left(ii\right):5+c=7\Rightarrow c=2$$

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