Question

can someone help me understand the quadratic formula and the discriminant.. with an example please :)

Answer 1

you ever complete a square?

Answer 2

the quadratic formula is the general result of completing the square .... as such, instead of working the process in a longhand version, we can simply go straight to the ending form of it.

Answer 3

The discriminant is meant to tell you if the solutions are distinct, repeated, or imaginary.

Answer 4

\[ax^2+bx+c=0\]
\[x^2+\frac bax+\frac ca=0\]
\[x^2+\frac bax=-\frac ca\]
\[x^2+\frac bax+(\frac{b}{2a})^2=(\frac{b}{2a})^2-\frac ca\]
\[(x+\frac{b}{2a})^2=(\frac{b}{2a})^2-\frac ca\]
\[x+\frac{b}{2a}=\pm\sqrt{(\frac{b}{2a})^2-\frac ca}\]
\[x=-\frac{b}{2a}\pm\sqrt{(\frac{b}{2a})^2-\frac ca}\]

Answer 5

with a little more simplification you would see that the quadrtic formula is the end result of the gneneral solution to the quadratic equation.

Answer 6

@iambatman

Answer 7

now if we simply ues the formula,

given ax^2 + bx+c=0

\[x=-\frac{b}{2a}\pm\frac{\sqrt{b^2-4ac}}{2a}\]
just fill in the required parts for abc

Answer 8

make what you have into the form: ax^2 + bx + c = 0 so that you can identify the required parts

Answer 9

the quadratic formula is so useful that they have even named parts of it

-b/2a is called the determinant, and b^2-4ac is called the discriminant.

-b/2a tells us the axis of symetry, and the b^2-4ac lets us know wht types of roots we have (real or complex)