1 / 8

Inequalities with Quadratic Functions

Inequalities with Quadratic Functions. 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.

jin
Télécharger la présentation

Inequalities with Quadratic Functions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Inequalities with Quadratic Functions Solving inequality problems

  2. Quadratic inequalities …means “for what values of x is this quadratic above the x axis” ax2+bx+c>0 e.g. x2+ x - 20 >0 …means “for what values of x is this quadratic below the x axis” ax2+bx+c<0 e.g. x2+ x - 20 < 0

  3. Pg 75 Q3 Inequality Problems (1) n(n+1) 2 The nth triangular number is given by: A) Find the value of n that gives the first triangular number over 100 B) What is the first triangular number over 100 C) Find the value of n that gives the first triangular number over 1000. What is it?

  4. Pg 75 Q3 n(n+1) 2 > 100 n = -1 [(-1)2 - (4 x 1 x -200)] 2 x 1 n = -1 [1 - -800] = -1 801 2 2 -14.65 13.65 Inequality Problems (1) n(n+1) 2 The nth triangular number is given by: A) Find the value of n that gives the first triangular number over 100 a = 1 b = 1 c = -200 n(n+1)>200 n2 + n > 200 n2 + n - 200 > 0 If n2 + n - 200 = 0 n = 13.65 or -14.65

  5. Pg 75 Q3 n(n+1) 2 > 100 n(n+1) 2 14(14+1) 2 -14.65 13.65 Inequality Problems (1) n(n+1) 2 The nth triangular number is given by: A) Find the value of n that gives the first triangular number over 100 n > 13.65 or n< -14.65 n =13.65 gives 100 n(n+1)>200 n2 + n > 200 n2 + n - 200 > 0 n =14 will give the integer solution over 100 B) What is the first triangular number over 100 = 14 x 15/2 = 105

  6. Pg 75 Q3 n(n+1) 2 > 1000 n = -1 [(-1)2 - (4 x 1 x -2000)] 2 x 1 n = -1 [1 - -8000] = -1 8001 2 2 -45.22 44.22 Inequality Problems (1) n(n+1) 2 The nth triangular number is given by: C) Find the value of n that gives the first triangular number over 1000. What is it? a = 1 b = 1 c = -2000 n(n+1)>2000 n2 + n > 2000 n2 + n - 2000 > 0 If n2 + n - 2000 = 0 n = 44.22 or -45.22 If n=45, number is 1035

  7. x = -8 [(8)2 - (4 x 2 x 7)] 2 x 2 = -2 2 2 Inequality Problems (2) A) Solve 2x2+ 8x +7 = 0 AQA 2002 Leaving answers as surds B) Hence solve 2x2+ 8x +7 > 0 Solve 2x2 + 8x +7 = 0 a = 2 b = 8 c = 7 x = -8 [64 - 56] = -8 8 4 4 = -8 22 4 x = -2 + 1/22 Or x = -2 - 1/22

  8. Inequality Problems (2) A) Solve 2x2+ 8x +7 = 0 AQA 2002 Leaving answers as surds B) Hence solve 2x2+ 8x +7 > 0 x = -2 + 1/22 Or x = -2 - 1/22 Or x < -2 - 1/22 x > -2 + 1/22

More Related