Question

If we express x^2 - 5x in the form a(x - h)^2 + k, then what is k?

Answer 1

Other method:

`f(x)=ax^2+bx+c=a(x-h)^2+k\\\\h=(-b)/(2a);\ k=f(h)=(-(b^2-4ac))/(4a)`
We have:

`f(x)+x^2-5x`
Therefore

`a=1;\ b=-5;\ c=0`
substitute

`h=(-(-5))/(2\cdot1)=(5)/(2)=2.5\\\\k=f(2.5)=2.5^2-5\cdot2.5=6.25-12.5=-6.25`
Your answer is:

`x^2-5x=(x-2.5)^2-6.25`

Answer 2

x² -5x
We need to complete square to write the equation x² -5x in a vertex form.
We will need to use formula a² - 2ab + b² = (a-b)²
x² -5x = x² -2*(5/2)x +(5/2)² - (5/2)² = (x-5/2)² - 25/4

Now we have
x² -5x = (x-5/2)² - 25/4.
We can see that they are the same graph.

If we compare (x-5/2)² - 25/4 and a(x-h)² + k, we can see that a=1, h= 5/2,
and k = -25/4 = - 6.25
k is y-coordinate of the vertex of the parabola.