Question

What is the improved quadratic formula in graphic form?

Answer 1

`x = -b/(2a) +- d/(2a)`
`D = d^2 = b^2 - 4ac`

Explanation:

The quadratic formula in graphic form (Socratic, Google Search):

`x = -b/(2a) +- d/(2a)`,
`D = d^2 = b^2 - 4ac`.

a, b, and c are the coefficients of the quadratic equation,
`-b/(2a)` is the coordinate of the axis of symmetry, or of the vertex
(+- d/2a) are the distances from the axis of symmetry to the 2 x-intercepts.
Example. Solve: `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 = 16/8 = 2`
`x2 = - 4/8 = - 1/2`