Question

Write the function in vertex form. identify the vertex.
y = 2x^2 - 4x + 5​

Answer 1

`\large\boxed{f(x)=2(x-1)^2+3}`

Explanation:

The vertex form of a quadratic function f(x) = ax² + bx + c:

`f(x)=a(x-h)^2+k`

Where (h, k) is a vertex.

`h=(-b)/(2a),\ k=f(h)`

We have:

`f(x)=2x^2-4x+5\to a=2,\ b=-4,\ c=5`

Calculate h and k:

`h=(-(-4))/(2(2))=(4)/(4)=1\\\\k=f(1)\to k=2(1^2)-4(1)+5=2-4+5=3`

Finally:

`f(x)=2(x-1)^2+3`