Hi everybody, I'm Raj Kainth from Mr.Piatek's 30S PreCal class and i am going to be blogging about the stuff we went over in today's class which is completing the square and how to find zeros of quadratic equations.

To turn a Quadratic Equation from standard form to a vertex form is called completing the square.

Example: f(x)=x^2-4x-3
1)Take the loose -3 and place it outside of bracket,leave (a) in front of brackets( which in this case is 1) and x^2-4x inside the bracket.
f(x)=(x^2-4x)-3
2)Take the coefficient (-4) ,divide it by 2 and square it.
-4=-4/2=-2=(-2)^2 =4

3)f(x)=(x^2 -4x+4)-3

4)"Balance" the equation by doing the opposite operation. If we add 4,then we also need to subtract 4 outside the bracket so that we do not affect the value of the equation.

f(x)=(x^2-4x+4)-3-4

5)Write ax+bx+c as a perfect square (x+c)^2 or (x-c)^2
f(x)=(x-2)^2-7

6)The quadratic equation is now in vertex form. Vertex @(h,k)or (2,-7)


Now i will show you how to find zeros.

Zeros are x-intercepts. At an x-intercept the value of (y)=O. To solve for the Os, make y=0, factor, write each factor equal to 0 and then solve.

Example: f(x) =x^2 -8x+12
y=x^2 -8x+12
0=x^2 -8x+12
0= (x-6)(x-2)
x-6=0 x-2=0
x=6 x=2

6 and 2 are both zeros
(6,0)-x-intercept-(2,0)
x-intercepts are written as coordinates

I hope this blog really helped you guys !!