Question

What are the advantages of the new improved Quadratic Formula in graphic form?

Answer 1

Improved Quadratic Formula

Explanation:

Improved Quadratic Formula in Graphic Form (Google, Yahoo, Bing Search). It can be also called "The Quadratic Formula in intercept form"
`x = - b/(2a) +- d/(2a)`
with `d^2 = b^2 - 4ac.`

Compared to the classical formula, the advantages are:

a. Simpler expression
b. Easier numeric computation, there for, less errors/mistakes.
c. Systematic steps to proceed.
d. Shows graphic interpretation and relationship between:
- The axis of symmetry and the 2 x-intercepts, and
- The distances from the axis of symmetry to the two x-intercepts.
Example of solving.
Solve: `y = 8x^2 - 22x - 13 = 0`
`D = d^2 = b^2 - 4ac = 484 + 416 = 900` --> `d = +- 30`
There are 2 real roots:
`x = -b/(2a) +- d/(2a) = 22/16 +- 30/16 = (11 +- 15)/8`
`x1 = 26/8 = 13/4`, and `x2 = - 4/8 = -1/2`