Inequations

ဒီအခန္းမွာေတာ့ Quadratic Inequations ေတြရဲ့ ေပးထားေသာ အေျခအေနကို ေျပလည္ေစမယ့္ solution set ကိုရွာမွာ ျဖစ္ပါတယ္။ Quadratic Inequations ေတြကို မေျဖရွင္းမီ Quadratic Function ဆိုတာကို သိရပါမယ္။

Quadratic Function

An expression f(x) = ax² + bx + c, where a, b, and c are numbers with a≠0 is

called a quadratic function.

ကိန္းရွင္တစ္ခုရဲ့ ႏွစ္ထပ္ကိန္း ပါ၀င္ေသာ function တစ္ခုကို quadratic function လို႔ေခၚပါတယ္။ Quadratic Function ရဲ့ characteristic က x² ပါ။ x² မပါရင္ quadratic function လို႔ မေျပာႏိုင္ပါဘူး။ ဒါေၾကာင့္ coefficient of x² ဟာ 0 မျဖစ္ရပါဘူး။

Quadratic Equation

ax² + bx + c = 0 is called a quadratic equation.

Solutions or Roots of Quadratic Equation





where a≠0









Graph of a Quadratic Function

The graph of a quadratic function is called a parabola. It is basically a curved shape opening up or down.



Quadratic Function တစ္ခုရဲ့ graph ကို parabola လို႔ေခၚပါတယ္။



When you have a quadratic function in the form f(x) = ax² + bx + c

if a > 0, then the parabola opens up ,

coefficient of x² ဟာ positive(a>0) ျဖစ္မယ္ဆိုရင္ graph ဆြဲတဲ့ အခါ open upward parabola ကိုရပါတယ္။

+x² => open upward parabola

if a <0, then the parabola opens down

coefficient of x² ဟာ positive(a<0) ျဖစ္မယ္ဆိုရင္ graph ဆြဲတဲ့ အခါ open downward parabola ကိုရပါတယ္။

- x² =>open downward parabola

Quadratic Inequations

The open sentences ax² + bx + c>0 and ax² + bx + c<0,a ≠ 0 are quadratic inequations in x.

The solution set of the quadratic inequations in x can be found by

(i) Algebraic method

(ii) Graphical method