notes/education/math/Quadratics.md

Notes

To convert an equation in the form of (x^2-3x) into a square equivalent, you half the second value, then square that value (in this case 3) (x-\frac{3}{2})^2, resulting in an equation like this.

 y = -5x^2 -20x + 13 

Given the above equation, you can factor out a -5, resulting in the equation -5(x^2+4x) + 13). Half of 4 is 2, and because the inside is multiplied by -5, -5 *4 = -20, so you add -20 to the other side to equalize the equation, resulting in an equation in the form of -20 + y = -5(x+2)^2+ 13. This simplifies down to y = -5(x+2)^2 + 33.

Forms

Standard form (vertex form)

 a(x - h)^2 + k 

To convert to standard form given a vertex of a quadratic equation and a point that falls along that line, plug values in for everything and solve for a.

Quadratic form

 y = a^2 + bx + c