How do you write a quadratic function in vertex form whose has vertex (1,2) and passes through point (2,4)?

1 Answer
Andy Y.
Jul 3, 2017

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

Explanation:

To solve this problem, you must know what the vertex form of a parabola is.

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

From this vertex-form of the quadratic equation, we are in a sense, given the vertex for free.

Vertex: #(h,k)#

You are given four values, #x,y,h,k#, which we can plug into this vertex form and solve for the remaining variable #a#.

#x=2#
#y=4#
#h=1#
#k=2#

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

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

#4=a+2#

#a=2#

With the last variable solved, we can finally plug in just our vertex, #(1,2)#,and the variable #a=2#, leaving the dependent variable #y# and independent variable #x# alone.

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

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