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

1 Answer
Aug 5, 2016

Answer:

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#
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