Question

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

Answer 1

Answer:

The vertex form will be:

$y(x)=(x-2)^{2}+1$

Step-by-step 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.

$y(x)=x^{2}-4x+(\frac{4}{2})^{2}-(\frac{4}{2})^{2}+5$

$y(x)=x^{2}-4x+4-4+5$

$y(x)=(x-2)^{2}-4+5$

Finally, the vertex form will be:

$y(x)=(x-2)^{2}+1$

I hope it helps you!