Question

What do the variables in the quadratic formula mean?

Answer 1

The quadratic formula uses the coefficients of the quadratic equation in standard form when it is equal to zero (y = 0). A quadratic equation in standard form looks like `y= ax^2 + bx + c`. The quadratic formula is `x = (-b +- sqrt(b^2 - 4ac))/(2a)`, when y = 0.

Here is an example of how the coefficients of the quadratic equation are used as variables in the quadratic formula:

`0 = 2x^2 + 5x + 3`
This means a = 2, b = 5, and c = 3.

So the quadratic formula becomes:
`x = (-5 +- sqrt(5^2 - 4(2)(3)))/(2*2)`

`x = (-5 +- sqrt(25 - 4(2)(3)))/(2*2)`

`x = (-5 +- sqrt(25 - 24))/(2*2)`

`x = (-5 +- sqrt(1))/(2*2)`

`x = (-5 +- 1)/(2*2)`

`x = (-5 +- 1)/(4)`

`x = (-5 + 1)/(4)` and `x = (-5 - 1)/(4)`

`x = -4/4 and x = -6/4`

`x = -1 and x = -3/2`