# x^2-20x+75=y (x-100)^25=y vertex= (100,-25)COMPLETE THE SQUARE CORRECTLY and show the mistake in the above work.

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For the equation x^2-20+75=y, we see that there is no term with x. If we are to complete the square there has to be a term with x.

I take the equation as

can rewrite it as: x^2 - 20x + 75 = y

=> x^2 - 20x + 75 + 25 = y + 25

=> x^2 - 20x + 100 = y + 25

=> (x - 10)^2 = y - (-25)

**Therefore the vertex is (10 , -25)**

I believe that the question should be as follow:

y= x^2 - 20x + 75

To complete the square, we will add and subtract ( x's coefficient/2)^2

==> We will add and subtract ( 20/2)^2 = 10^2 = 100

==> y= x^2 - 20x + 75 + 100 - 100

We will rearrange terms.

==> y= x^2 - 20x + 100 + 75 - 100

Now we will write the complete square.

**==> y= (x-10)^2 - 25 **