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# parabola

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Find the equation of the parabola that passes through (4,-7) and has vertex (1,-6)

Oct 2, 2020

#1
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Find the equation of the parabola that passes through (4,-7) and has vertex (1,-6)

Hello Guest!

$$P_{v}(1,-6)\\ P_1 (4,-7)$$

Because of the symmetry

$$P_2(-2,-7)$$

$$\large y=ax^2+bx+c$$

$$c=-6\ (vertex)$$

$$-6=\ a\ +\ b\ -\ 6$$      | $$\times 4$$

$$-24=4a+4b-24$$     | subtr.

$$\underline{-7=16a+4b-6}$$

$$17=12a+18\\ \ a\ =\frac{17-18}{12}$$

$$a=-\frac{1}{12}$$

$$-6=-\frac{1}{12}+b-6$$

$$b=\frac{1}{12}$$

$$The\ equation\ of\ the\ parabola\ is$$  $$y=-\frac{1}{12}x^2+\frac{1}{12}x-6$$

!

Oct 2, 2020
edited by asinus  Oct 2, 2020
edited by asinus  Oct 3, 2020