**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.

QUADRATIC EQUATIONS:

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

quadratic equation include 2x |
2+3x-5=0. |

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.

*QUADRATIC* INEQUALITIES:

*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.

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