## anonymous 4 years ago how do you complete the square

1. anonymous

depends on the context. are you trying to solve a quadratic equation?

2. anonymous

no parabolas

3. anonymous

they are the same thing

4. anonymous

ah then you want to find the vertex by comleting the square. i.e. you want to write $y=ax^2+bx+c$ as $y=a(x-h)^2+k$ right

5. anonymous

$x^2 +bx+c=x^2+bx+(b/2)^2-(b/2)^2+c=(x+b/2)^2+c-(b/2)^2$

6. anonymous

here is an easy method with an example. the vertex is always where $x=-\frac{b}{2a}$ so if i see $y=x^2-6x+5$ i know the first coordinate of the vertex will be $-\frac{6}{2(-1)}=3$ and the second coordinate will be what i get when i replace x by 3 namely -4 so i know it is $y=x^2-6x+5=(x-3)^2-4$

7. anonymous

here is another method. if you have $y=ax^2+bx+c$ you can rewrite as $y=a(x^2+\frac{b}{a}x)+c$ and then write $y=a(x+\frac{b}{2a})^2+c-\frac{b^2}{4a}$ but that seems unnecessarily complicated