Quadratic inequalities

Solve:

 $2x^2+5x-12≥0$  

•  $-4\le x\le1.5$ 

•  $x<-4\ or\ x>1.5$ 

•  $x\le-4\ or\ x\ge1.5$  

• no solution

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

Solve: 

 $5x-10x^2<0$  

•  $0<x<.5$  (0, ½)

•  $0\le x\le.5$ 

•  $x<0\ or\ x>.5$ 

•  $-.5<x<0$ 

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.4

Solve:

 $3x-x^2>0$  

•  $x<0\ \ or\ \ x>3$ 

•  $x<-3\ \ or\ \ x>0$ 

•  $-3<x<0$ 

•  $0<x<3$ 

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

• $y≥-(x+4)²+1$

• $y<-(x-4)²+1$

• $y≤(x-4)²+1$

• $y≤-(x-4)²+1$

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.C.7

CCSS.HSA.REI.D.10

• $y≤(x-3)²+3$

• $y<(x+3)²-3$

• $y<(x-3)²-3$

• $y≤(x+3)²-3$

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

CCSS.HSA.REI.D.12

Solve:

 $6x^2-54≤0$  

•  $-3≤x≤3$  

•  $x≤-3\ \ or\ \ x≥3$  

•  $-3<x<3$  

•  $x<-3\ \ or\ \ x>3$  

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

Solve:

 $2x^2+9x-143<0$  

•  $-11<x<6.5$  

•  $-11≤x≤6.5$  

• no solution

• all reals

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.4

 $x^2-9x-112≥0$  

•  $-7<x<16$  

•  $-7≤x≤16$  

•  $x<-7\ \ or\ \ x>16$  

•  $x≤-7\ \ or\ \ x≥16$  

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

 $-3x^2-6x+45≥0$  

•  $-5<x<3$  

•  $-5≤x≤3$  

•  $x<-5\ \ or\ \ x>3$  

•  $x≤-5\ \ or\ \ x≥3$  

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

 $4x^2-8x-77<0$  

•  $-3.5<x<5.5$  

•  $-2.5<x<7.5$  

•  $-4<x<8$  

•  $-6<x<8$  

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4