How do I change something from the ax^2+bx+c form to a(x-h)^2+k form?

Question

anonymous · Answer

h is the axis of symmetry of the parabola, so what you can do is solve for the equation $$x = \frac{-b}{2a}$$ and that will be your h

to find the k, simply evaluate the equation ax^2 + bx + c at x = h

anonymous · Answer

example:$$x^2 + 2x + 1$$finding h $$h = \frac{-b}{2a}=\frac{-2}{2}=-1$$

finding k$$1 - 2 + 1 = 0$$

therefore our new equation is$$(x + 1)^2$$

nikvist · Answer

$$ax^2+bx+c=a\left(x^2+\frac{b}{a}x+\frac{c}{a}\right)=a\left(\left(x+\frac{b}{2a}\right)^2-\frac{b^2}{4a^2}+\frac{c}{a}\right)=$$$$=a\left(x+\frac{b}{2a}\right)^2-\frac{b^2}{4a}+c=a\left(x-\underbrace{\left(-\frac{b}{2a}\right)}_h\right)^2+\underbrace{\frac{4ac-b^2}{4a}}_k$$