This document discusses solving quadratic inequalities by graphing. It explains that the best method is to draw the graph of the quadratic function and find where it is positive and negative based on the roots. The roots are found by factorizing the quadratic expression. Several examples are worked through step-by-step to demonstrate this process. Key questions are provided for students to practice solving various quadratic inequalities graphically.
9. Solve x2
+ x – 6 > 0
Need graph y = xy = x22
+ x – 6+ x – 6
Find RootsFind Roots FactoriseFactorise
(x + 3)(x – 2)(x + 3)(x – 2)
roots x= -3 or 2roots x= -3 or 2
10. 22
Solve x2
+ x – 6 > 0
Roots x = -3 or 2
-3-3
xx22
+ x – 6 > 0+ x – 6 > 0
y = xy = x22
+ x – 6+ x – 6
y positivey positive
y negativey negative
11. 22
Solve x2
+ x – 6 > 0
Roots x = -3 or 2
-3-3
xx22
+ x – 6 > 0+ x – 6 > 0
y = xy = x22
+ x – 6+ x – 6
y positivey positive
y negativey negative
x < -3x < -3 and x > 2and x > 2
12. Solve:
1. x2
– 5x + 6 < 0
2. x2
– 2x – 8 > 0
3. x2
– 16 < 0
4. x2
– 10x > 0
5. 10x – x2
> 0
6. x2
– 3x – 18 ≥ 0
7. 2x2
– 8x + 6 ≤ 0
8. x2
+ 8x + 16 < 0
9. x2
+ 8x + 16 ≤ 0
10. x2
+ 8x + 16 > 0 .
2 < x < 32 < x < 3
x > 4 or x < -2x > 4 or x < -2
Key QuestionKey Question
x > 10 or x < 0x > 10 or x < 0
0 < x < 100 < x < 10
xx ≥ 6 or x6 or x ≤ -2-2
11 ≤ xx ≤ 33
13. x2
– 16 < 0
Factorising (x – 4)(x + 4)
Roots x = 4 and x = -4
Key QuestionKey Question
44-4-4
-4 < x < 4-4 < x < 4