What is the equation of the parabola that has a vertex at # (-5, -4) # and passes through point # (5,396) #?

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What is the equation of the parabola that has a vertex at # (-5, -4) # and passes through point # (5,396) #?

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Answer 1 · 2015-12-24T09:45:23

# y = 4x^2 +40x +96#

Explanation:

The equation of a parabola, written in vertex form, is #y = n(x - h)^2 +k# where (h,k) are the coordinates of the vertex.
For this example then, #y = n(x+5)^2 -4#
To find n, we substitute in the coordinates of the given point.
#396 = n(5 +5)^2 -4#
#400 = 100n#
#n = 4#
Thus the equation is #y = 4(x+5)^2 -4#
or in standard form # y = 4x^2 +40x +96#

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What is the equation of the parabola that has a vertex at # (-5, -4) # and passes through point # (5,396) #?

1 Answer

Explanation:

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