Inequalities Quadratic

Quadratic inequalities KUS objectives BAT Solve quadratic and linear inequalities BAT solve inequalities problems in context Starter: Solve 𝒙 𝟐 >𝟏𝟔 Solve 𝒙 𝟐 −𝟏< 𝟖 Solve (𝒙+𝟑) 𝟐 ≥ 𝟖𝟏

Starter: inequalities notation 3 Starter: x squared greater than 16 Starter: inequalities notation 3 If Then 16 -4 4

Starter: inequalities notation 3 Starter: x squared less than 9 Starter: inequalities notation 3 If Then 9 -3 3

Starter: inequalities notation 3 If Then or 81 𝑥≤−12 𝑜𝑟 𝑥≥6 -3 6 -12

𝑥<−4 𝑜𝑟 𝑥>4 −3<𝑥<3 𝑥≤−12 𝑜𝑟 𝑥≥6 2 4 6 8 -2 -4 -1 1 2 3 -2 Starter: summary of results 2 4 6 8 -2 -4 Solve 𝒙 𝟐 >𝟏𝟔 𝑥<−4 𝑜𝑟 𝑥>4 Solve 𝒙 𝟐 −𝟏< 𝟖 -1 1 2 3 -2 -3 −3<𝑥<3 Solve (𝒙+𝟑) 𝟐 ≥ 𝟖𝟏 -3 3 6 9 -6 -9 -12 𝑥≤−12 𝑜𝑟 𝑥≥6

Starter: inequalities notation 3 Factorise and solve i Starter: inequalities notation 3 WB 3a Factorise Gives Solve Gives

Starter: inequalities notation 3 Solve quad inequality i Starter: inequalities notation 3 WB 3a Solve 𝒙 𝟐 +𝟕𝒙−𝟏𝟖 >𝟎 Answers above zero Then roots -9 2 x values that work

Starter: inequalities notation 3 Factorise and solve ii Starter: inequalities notation 3 WB3b Factorise Gives Solve Gives

Starter: inequalities notation 3 WB 3b Solve 𝒙 𝟐 −𝟖𝒙+𝟏𝟐≤𝟎 Then roots 2 6 x values that work Answers below or equal to zero

Then Solve quad inequality ii Solve −𝒙 𝟐 +𝟑𝒙+𝟏𝟎>𝟎 WB 4a what to do if coefficient of x squared is negative part I Solve −𝒙 𝟐 +𝟑𝒙+𝟏𝟎>𝟎 Answers greater than zero −[ 𝒙 𝟐 −𝟑𝒙−𝟏𝟎] >𝟎 Then roots -2 5 x values that work

Then Solve quad inequality ii Solve −𝒙 𝟐 +𝟑𝒙+𝟏𝟎>𝟎 𝒙 𝟐 −𝟑𝒙−𝟏𝟎 <𝟎 WB 4b what to do if coefficient of x squared is negative part II Solve −𝒙 𝟐 +𝟑𝒙+𝟏𝟎>𝟎 Answers less than zero 𝒙 𝟐 −𝟑𝒙−𝟏𝟎 <𝟎 Then roots -2 5 x values that work

Starter: inequalities notation 3 Practice Starter: inequalities notation 3 Solve these Inequalities. Draw a graph to help you each time

WB 5 i) Solve 5x – 2 > 3x + 7 Solve 𝒙 𝟐 −𝟕𝒙−𝟏𝟖<𝟎 Solve to find when both inequalities hold true i) Solve 5x – 2 > 3x + 7 Solve 𝒙 𝟐 −𝟕𝒙−𝟏𝟖<𝟎 5 6 7 8 9 4 3 5 6 7 8 9 4 3 2 1 -1 -2 iii) Solve to find when both inequalities hold true

WB 6 Problem In context The specification for a new rectangular car park states that the length L is to be 18 m more than the breadth and the perimeter of the car park is to be greater than 68 m The area of the car park is to be less than or equal to 360 m2 Form two inequalities and solve them to determine the set of possible values of L 𝑳 𝑳−𝟏𝟖 ≤𝟑𝟔𝟎 𝑳 𝟐 −𝟏𝟖𝑳 −𝟑𝟔𝟎≤𝟎 (𝑳+𝟏𝟐) 𝑳−𝟑𝟎 ≤𝟎 -12 ≤ 𝑳≤𝟑𝟎 𝟐𝑳+𝟐 𝑳−𝟏𝟖 >𝟔𝟖 𝟒𝑳−𝟑𝟔>𝟔𝟖 𝑳>𝟐𝟔 Combined solutions gives 26 < 𝑳≤𝟑𝟎

Label the intersections and solution on your sketch WB6 Challenge double quadratics ! Sketch a graph to show the simultaneous solution to both these inequalities 𝑥 2 −3𝑥−10<0 and 𝑥 2 +𝑥+6>0 Label the intersections and solution on your sketch

One thing to improve is – KUS objectives BAT Solve quadratic and linear inequalities BAT solve inequalities problems in context self-assess One thing learned is – One thing to improve is –

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