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

1 Answer
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