What is the improved quadratic formula in graphic form?

1 Answer
Nghi N
Jul 9, 2017

The improved quadratic formula in graphic form:
#x = - b/(2a) +- d/(2a)#
#D = d^2 = b^2 - 4ac#.

Explanation:

This formula relates the 2 roots of the quadratic equations to the parabola graph of the function y = ax^2 + bx + c.

#x = - b/(2a) +- d/(2a)#
with #d^2 = D = b^2 - 4ac#.
In this formula,
- the quantity #(-b/(2a))# represents the x-coordinate of the axis of symmetry.
- The 2 quantities #(+- d/(2a))# represent the 2distances from the axis of symmetry to the 2 x-intercepts.
Advantages:
- Simpler expression, and easier to remember because students can relate the formula to the parabola graph.
- Simple steps for easier numeric computation.
Example. Solve: #y = 16x^2 - 62x + 21 = 0#.
#D = d^2 = b^2 - 4ac = 3844 - 1344 = 2500# --> #d = +- 50#
There are 2 real roots:
#x = 62/32 +- 50/32= (31 +- 25)/16#
#x1 = 56/16 = 7/2#, and #x2 = 6/16 = 3/8#

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