Respuesta :

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.
Ver imagen mkryukova19
Ver imagen mkryukova19
gmany
Other method:
[tex]f(x)=ax^2+bx+c=a(x-h)^2+k\\\\h=\dfrac{-b}{2a};\ k=f(h)=\dfrac{-(b^2-4ac)}{4a}[/tex]
We have:
[tex]f(x)+x^2-5x[/tex]
Therefore
[tex]a=1;\ b=-5;\ c=0[/tex]
substitute
[tex]h=\dfrac{-(-5)}{2\cdot1}=\dfrac{5}{2}=2.5\\\\k=f(2.5)=2.5^2-5\cdot2.5=6.25-12.5=-6.25[/tex]
Your answer is:
[tex]x^2-5x=(x-2.5)^2-6.25[/tex]

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