QUADRATIC
INEQUALITIES
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Si Medusa at ang kanyang dalawang kapatid na babae ay tinatawag na Gorgon. Sila’y mga pangit na babae at nakatatakot tingnan. Si Medusa ay hindi dating pangit na babae. Noong kaniyang kabataan, siya ay magangdang-maganda. Doon siya nakatira sa dakong hilaga ng daigdig na hindi sinisikatan ng araw. Ipinakiusap niya kay Atena na siya ay hayaang tumira sa dakong timog na laging sinisikatan ng araw. Hindi siya pinaunlakan ng diyosa. Nagalit si Medusa. Sinabi niyang iyon, pinarusahan siya ni Atena. N
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QUADRATIC
INEQUALITIES
OBJECTIVES:
Illustrates and solve quadratic inequalities; and identify the solution of inequality by using graph
SHOW ME
Write the mathematical symbol inside the box. GREATER THAN
SHOW ME
Write the mathematical symbol inside the box. LESS THAN
SHOW ME
Write the mathematical symbol inside the box. LESS THAN OR EQUAL TO
QUADRATIC INEQUALITY A quadratic inequality is an inequality that contains a polynomial of degree 2 and can be written in any of the following forms: ax² + bx + c > 0 ax² + bx + c < 0 ax² + bx + c ≥ 0 ax² + bx + c ≤ 0 Where a, b and c are real numbers and a≠
Example:
NOT QUADRATIC INEQUALITY 5xᵌ + 10x + 6 > 0 4x ( x² + 8 ) < - 1 3 ( x + 8 ) ≥ x - 6 3x ( x - 2 ) + 1 ≥ x⁴ - 6
Solving Quadratic Inequalities
Continuation of Example 1 Critical points: 4 and 2
x²- 6x + 8 < 0
Since hollow Circle , Critical points 4 and 2 are not included for the solution set 4²- 6(4) + 8 < 0 x²- 6x + 8 < 0 0 < 0 (^) False x²- 6x + 8 < 0 2²- 6(2) + 8 < 0 16 - 24 + 8 < 0 4 - 12 + 8 < 0 0 < 0 False
Continuation of Example 1
x²- 6x + 8 < 0
Critical points: 4 and 2 Test points: 0, 3 and 5 -----------------False-------------- --True-- --False-- Solution Set using Interval Notation: (2,4) Solution Set { 2 < x < 4}
Continuation of Example 2 Critical points: -4 and - Since hollow Circle , Critical points -4 and -2 are not included for the solution set (-4)²+ 5(-4) + 4 > 0 x²+5x + 4 > 0 0 > 0 (^) False
0 < 0 False
x²+ 5x + 4 > 0
x²+5x + 4 > 0
Continuation of Example 2 Critical points: -4 and -1 (^) Test points: -5, -3 and 0 --True-- ----False---- Solution Set using Interval Notation: (-4,-1) Solution Set { x < -4 or x -1}
x²+ 5x + 4 > 0
x²+5x + 4 > 0 (^) x²+5x + 4 > 0 x²+5x + 4 > 0 (-5)²+ 5(-5) + 4 > 0 (^) (-3)²+ 5(-3) + 4 > 0 (0)²+ 5(0) + 4 > 0 25 - 10 + 4 > 0 9 - 15 + 4 > 0 (^) 0 + 0 + 4 > 0 9 > 0 (^) -2 > 0 4 > 0 ----------------True------------ --Region1-- ----Region 2---- -------------Region 3----------