Question

Convert y=x^2-4x+5 to vertex form by completing the square

Answer 1

The vertex form will be:

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

Explanation:

The equation of the vertex form of a quadratic equation is given by:

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

Where:

a is a coefficient

h is the x value of the vertex

k is the y value of the vertex

To completing the square we just need to add and subtract the square of the term with x divided by 2.

`y(x)=x^(2)-4x+((4)/(2))^(2)-((4)/(2))^(2)+5`

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

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

Finally, the vertex form will be:

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

I hope it helps you!