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

Aug 5, 2016

#### Explanation:

Improved Quadratic Formula in Graphic Form (Google, Yahoo, Bing Search). It can be also called "The Quadratic Formula in intercept form"
$x = - \frac{b}{2 a} \pm \frac{d}{2 a}$
with ${d}^{2} = {b}^{2} - 4 a c .$

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: $y = 8 {x}^{2} - 22 x - 13 = 0$
$D = {d}^{2} = {b}^{2} - 4 a c = 484 + 416 = 900$ --> $d = \pm 30$
There are 2 real roots:
$x = - \frac{b}{2 a} \pm \frac{d}{2 a} = \frac{22}{16} \pm \frac{30}{16} = \frac{11 \pm 15}{8}$
$x 1 = \frac{26}{8} = \frac{13}{4}$, and $x 2 = - \frac{4}{8} = - \frac{1}{2}$