What is the quadratic equation containing (5, 2) and vertex (1, –2)?

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Answer 1 · 2014-11-12T23:05:15

Vertex Form

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

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

By Vertex Form with #(h,k)=(1,-2)#, we have

#y=a(x-1)^2-2#

By plugging in #(x,y)=(5,2)#,

#2=a(5-1)^2-2=16a-2#

by adding #2#,

#=> 4=16a#

by dividing by #16#,

#=> 1/4=a#

Hence, the quadratic equation is

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

I hope that this was helpful.