How do I use completion of the square to solve a quadratic function?
I'll use an example to illustrate this:"find the roots of x2+6x-15"The advantage of completing the square for a quadratic is that it also gives the turning point of the parabola.Here, we're looking to factorize the expression as much as possible.(x+3)(x+3) = x2+6x+9This is close to our function, but not quite there yet!(x+3)2-9-15 = x2+6x-15 Therefore completing the square gives: x2+6x-15 = (x+3)2-24To find the roots of this, solve for x. As we have a square function, we will obtain 2 solutions when solving: one positive, one negative. These 2 solutions are the roots of the quadratic function. Now, for the turning point of the parabola: this is when (x+3)2 is at a minimum, in other words when x= -3. The y value for the minimum is -24.
