Graphical Method to Find the Solution Set of a Quadractic Equation

1. ေပးထားေသာ Function ကို y ဟုထားပါ။
2. y=0 ထားၿပီး X-axis ျဖတ္မွတ္မ်ားကို ရွာပါ။
3. x=0 ဟုထားၿပီး Y-axis ျဖတ္မွတ္ကို ရွာပါ။
4. ျဖတ္မွတ္မ်ားကို အသံုးျပဳၿပီး smooth parabola ဆြဲပါ။
5. ေပးေထားေသာ inequation sign ကို ၾကည့္ၿပီး solution set ကို ဆံုးျဖတ္ပါ။

Example 1

Use a graphical method, to find the solution set of the inequation 12 - 5x - 2x² ≥ 0 and illustrate it on the number line.





Solution

Let y=12 - 5x - 2x²

When y = 0,

12 - 5x - 2x² = 0

(4 + x)(3 - 2x) = 0

x = -4 or x = 3/2

Therefore, the graph cuts the X-axis at (-4,0) and (3/2,0).

When x = 0, y = 12

Therefore, the graph cuts the Y-axis at (0,12).



The solution set of 12 - 5x - 2x² ≥ 0 is {x/-4 ≤ x ≤ 3/2}.









Example 2

Find the solution set of the inequation 3x² < x² - x + 3 by graphical method and illustrate it on the number line.



Solution

3x² < x² - x + 3

2x² + x - 3 <0

Let y=2x² + x - 3

When y = 0,

2x² + x - 3 = 0

(2x + 3)(x - 1) = 0

x = - 3/2 or x = 1

Therefore, the graph cuts the X-axis at (-3/2,0) and (1,0).

When x = 0, y = -3

Therefore, the graph cuts the Y-axis at (0,-3).



The solution set of 3x² < x² - x + 3 is {x/-3/2 < x <1}.>







Example 3

Find the solution set of the inequation 12x² ≥ 10 - 7x by graphical method and illustrate it on the number line.



Solution

12x² ≥ 10 - 7x

12x² + 7x - 10 ≥ 0

Let y=12x² + 7x - 10

When y = 0,

12x² + 7x - 10= 0

(4x + 5)(3x - 2) = 0

x = - 5/4 or x = 2/3

Therefore, the graph cuts the X-axis at

(- 5/4,0) and (2/3,0).

When x = 0, y = -10

Therefore, the graph cuts the Y-axis at (0,-10).



The solution set of 3x² < x² - x + 3 is {x/ x ≤- 5/4 or x ≥ 2/3}.