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# parabola

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A parabola with equation y = x^2 + bx + c  passes through the points (-1,-11) and (3,18). What is c?

Oct 14, 2020

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A parabola with equation y = x^2 + bx + c passes through the points (-1,-11) and (3,18). What is c?

Hello Guest!

$$y=x^2+bx+c\\ P_1(-1,-11)\\ P_2\ (3,18)$$

$$-11=1-b+c\\ 18=9+3b+c\\$$

$$c=-11-1+b=18-9-3b\\ 4b=18-9+1+11$$

$$b=5.25$$

$$c=18-9-3b\\ c=18-9-3\cdot 5.25$$

$$c=-6.75$$

The parabola has the equation $$y=x^2+5.25x-6.75$$

Oct 14, 2020