What is the equation of the parabola that has a vertex at # (-1, 4) # and passes through point # (2,13) #?

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What is the equation of the parabola that has a vertex at # (-1, 4) # and passes through point # (2,13) #?

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Answer 1 · 2016-09-04T16:22:04

The equation is #y = (x + 1)^2 + 4#

Explanation:

In vertex form, #y = a(x - p)^2 + q#, the vertex is located at #(p,q)# and a point on the function is #(x, y)#. We will need to solve for the parameter #a#.

#y = a(x - p)^2 + q#

#13 = a(2 - (-1))^2 + 4#

#13 = a(9) + 4#

#13 = 9a + 4#

#9 = 9a#

#a = 1#

Hence, the equation of the parabola is #y = (x + 1)^2 + 4#

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What is the equation of the parabola that has a vertex at # (-1, 4) # and passes through point # (2,13) #?

1 Answer

Explanation:

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