What is the equation of the parabola that has a vertex at # (2, 3) # and passes through point # (-1,-2) #?

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What is the equation of the parabola that has a vertex at # (2, 3) # and passes through point # (-1,-2) #?

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Answer 1 · 2016-02-06T12:35:51

The Equation of the Parabola is # y= a(x-h)^2+3# where (h,k) is the vertex. So #y=a(x-2)^2+3# Now the equation passes through the point (-1,-2) So #-2=a(-1-2)^2+3 or -2 =9*a+3 or 9*a=-5 or a=-5/9#
So the equation of the Parabola becomes #y=-5/9(x^2-4*x+4)+3#
or #y= -5/9*x^2 +20/9*x+7/9# graph{-5/9x^2+20/9x+7/9 [-10, 10, -5, 5]} [Ans]

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What is the equation of the parabola that has a vertex at # (2, 3) # and passes through point # (-1,-2) #?

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