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 a0 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 a0




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