How do you find the rule of a quadratic function whose graph has given vertex of (4,5) and passes through the given point of (6,17)?

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Answer 1 · 2016-10-31T16:50:59

You have not given enough information to rule out one of two possible configurations. Please see the explanation.

There are two possible configurations:

#y = a(x - h)^2 + k#

and

#x = a(y - k)^2 + h#

where #(h, k)# is the vertex.

Substituting the vertex, #(4,5)#, and the point #(6,17)# into both and then solving for the respective values of a:

#17 = a(6 - 4)^2 + 5#

and

#6 = a(17 - 5)^2 + 4#

Solve for a:

#a = 3#

and

#a = 1/72#

The two possible equations are:

#y = 3(x - 4)^2 + 5#

and

#x = 1/72(y - 5)^2 + 4#