What is the equation of the parabola that has a vertex at # (4, -3) # and passes through point # (31,-4) #?

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What is the equation of the parabola that has a vertex at # (4, -3) # and passes through point # (31,-4) #?

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Answer 1 · 2016-07-10T03:16:45

For problems like this, use vertex form #y = a(x - p)^2 + q#, where #(x, y)# is the point on the function, #(p, q)# is the vertex, and #a# influences the breadth of the parabola. We will be solving for #a#.

#-4 = a(31 - 4)^2 - 3#

#-4 = 729a - 3#

#-1 = 729a#

#-1/729 = a#

Hence, the equation of the parabola is #y = -1/729(x - 4)^2 - 3#

Hopefully this helps!

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What is the equation of the parabola that has a vertex at # (4, -3) # and passes through point # (31,-4) #?

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