# 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}.

စာဖတ်သူ၏ အမြင်ကို လေးစားစွာစောင့်မျှော်လျက်!