Question

1. Rewrite f(x) = 2x^2 - 4x + 5 to its vertex form

Answer 1

Given

`f(x)=2x^2-4x+5`

To rewrite in vertex form.

Now,

The vertex form of a quadratic equation is given by,

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

Here, (h, k) is the vertex of the equation.

Then,

`\begin{gathered} f(x)=2x^2-4x+5 \\ =2(x^2-2x)+5 \\ =2(x-(2)/(2))^2-2+5 \\ =2(x-1)^2+3 \end{gathered}`

Hence, the vertex form of the equation is 2(x-1)^2+3.