Rewrite the equation in Vertex form. y=x^2-2x-63

Question

Is there a different method other than completing the square to solve this? 

Answer 1

Hi Yo, completing the square is the fastest method to use to write the equation in vertex form.

 

Remember that (x-h)² = x² - 2xh + h². 

 

We can apply this observation to your problem. The -2x in the problem statement is equal to -2xh. That allows us to solve for h very easily where h = 1.

-2x = -2xh    (divide both sides by -2x)

1 = h

 

When we add h² to the problem, we need to remember to subtract it as well. I encourage my students to set up their problem like this:

(x² - 2x + _______) - 63 - _______

(x² - 2x + ___1___) - 63 - ___1___

From here we can easily simplify to vertex form:

y= (x-1)² - 64

 

This gives the coordinates of the vertex as (1, -64).

 

I hope this helps!

Lindsey