PARABOLA GRAPHS

It refers to mathematical graph that has been useful in various fields in real life. They are applied in space travel and baseball sports. In other terms, parabola is the shape formed by an item thrown in the sky. The structural engineers have applied the concept in other fields such as in building suspension bridges. In addition, the vehicle headlights are parabolic to ensure that light from the bulb is reflected proportionally and parallel to the reflector. The idea is further utilized in satellite dishes, telescopes etc.

The equations take a general form of ax2 +bx+c=0, where a, b and c are coefficients, “a” is not equal to zero, otherwise it would be linear equation of the form bx+c=0. An example of a

Using the factoring method, we can solve the equation above as follows:

2×2+3x-5=0 can be factored as 2×2+5x-2x-5=0

Then simplified as x (2x+5) +1(2x+5) =0

(x-1)(2x+5)=0

This follows x-1=0 or 2x+5=0

Parabola Graphs

Hence x=1 or -2.5.

These inequalities take a general form of ax2 +bx+c≥∕≤0. For example x2-2x-3<0, using the factoring method, the inequality is solved as follows: the first step involves changing the inequality sign to an equal sign x2-2x-3=0.

Factoring x2-2x-3=0 becomes x2-3x+x-3=0

Then simplified as follows x(x-3) +1(x-3) =0

(x+1)(x-3)=0

X=-1 or 3.

## References:

Stillwell, J (2004), Mathematics and its History Springer-Verlag publishers, Berlin and New York.