Inequalities with Quadratic Functions Solving inequality problems Solving inequality problems.

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Presentation transcript:

Inequalities with Quadratic Functions Solving inequality problems Solving inequality problems

Quadratic inequalities …means “for what values of x is this quadratic above the x axis” ax 2 +bx+c>0 e.g. x 2 + x - 20 >0 …means “for what values of x is this quadratic below the x axis” ax 2 +bx+c<0 e.g. x 2 + x - 20 < 0

Inequality Problems (1) The n th triangular number is given by: n(n+1) 2 A) Find the value of n that gives the first triangular number over 100 B) What is the first triangular number over 100 Pg 75 Q3 C) Find the value of n that gives the first triangular number over What is it?

Inequality Problems (1) The n th triangular number is given by: n(n+1) 2 A) Find the value of n that gives the first triangular number over 100 Pg 75 Q3 n(n+1) 2 > 100 n(n+1)>200 n 2 + n > 200 n 2 + n > 0 If n 2 + n = 0 a = 1 b = 1 c = -200 n = -1   [(-1) 2 - (4 x 1 x -200)] 2 x 1 n = -1   [ ] = -1   n = or

Inequality Problems (1) The n th triangular number is given by: n(n+1) 2 A) Find the value of n that gives the first triangular number over 100 Pg 75 Q3 n(n+1) 2 > 100 n(n+1)>200 n 2 + n > 200 n 2 + n > n > or n< n =13.65 gives 100 n =14 will give the integer solution over 100 B) What is the first triangular number over 100 n(n+1) 2 14(14+1) 2 = 14 x 15/2 = 105

Inequality Problems (1) The n th triangular number is given by: n(n+1) 2 C) Find the value of n that gives the first triangular number over What is it? Pg 75 Q3 n(n+1) 2 > 1000 n(n+1)>2000 n 2 + n > 2000 n 2 + n > 0 If n 2 + n = 0 a = 1 b = 1 c = n = -1   [(-1) 2 - (4 x 1 x -2000)] 2 x 1 n = -1   [ ] = -1   n = or If n=45, number is 1035

Inequality Problems (2) AQA 2002 Solve 2x 2 + 8x +7 = 0 Leaving answers as surds B) Hence solve 2x 2 + 8x +7 > 0 A) Solve 2x 2 + 8x +7 = 0 a = 2 b = 8 c = 7 x = -8   [(8) 2 - (4 x 2 x 7)] 2 x 2 x = -8   [ ] = -8   x = / 2  2 = -8  2  2 4 = -2   2 2 Or x = / 2  2

Inequality Problems (2) AQA 2002 Leaving answers as surds B) Hence solve 2x 2 + 8x +7 > 0 A) Solve 2x 2 + 8x +7 = 0 x = / 2  2 Or x = / 2  2 x > / 2  2 Or x < / 2  2