Question

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

Answer 1

`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`