Quadratic Inequalities

Solve the quadratic inequality.

 $x^2+6x+8>0$  

•  $-4<x<-2$ 

•  $x<-4$ 

•  $x>-2$ 

•  $x<-4\$ or  $x>-2$ 

Solve the quadratic inequality.

 $x^2-2x-15<0$  

•  $-3<x<5$ 

•  $x<-3$ 

•  $x>5$ 

•  $x<-3$ or  $x>5$ 

Solve the quadratic inequality.

 $x^2-2x-8\le0$  

•  $-2\le x\le4$ 

•  $-2<x<4$ 

•  $-4\le x\le2$ 

•  $x\le-2$ or  $x\ge4$ 

 $x^2+2x\ge3$  

•  $x\le-3$  or  $x\ge1$  

•  $-3\le x\le1$  

•  $-1\le x\le3$  

•  $x\le-1$  or  $x\ge3$  

 $x^2-4x+3\ge0$  

•  $x<1$  or  $x>3$  

•  $1\le x\le3$  

•  $-3\le x\le-1$  

•  $x\le1$  or  $x\ge3$  

Solve the quadratic equation

 $x^2+12x+23=0$  

•  $\pm6-\sqrt{23}$  

•  $6\pm\sqrt{13}$  

•  $-12+\sqrt{23}$  

•  $\pm\sqrt{13}-6$  

Work backwards: what is the quadratic equation given the solutions

 $x\ =\pm\sqrt{14}-5$  

•  $\left(x+5\right)^{2\ }=14$  

•  $\left(x-14\right)^2=5$  

•  $\left(x-5\right)^2=14$  

•  $\left(x+14\right)^2=5$  

Knowing the answer from the last question multiply out

 $\left(x+5\right)^2=14$  

•  $x^2+25=14$  
  

•  $x^2+10x+25=14$  
  

•  $x^2-10x+25=14$  
  

•  $x^2-10x-25=14$  
  

Use the answer from the last problem set the equation equal to 0

 $x^2+10x+25=14$  

•  $x^2+10x+39=0$  
  

•  $x^2+10x-11=0$  
  

•  $x^2+10x+11=0$  
  

•  $x^2+10x-39=0$  
  

 $x=\pm\sqrt{7}+6$  

Use what you know to build the equation for the given answers:

•  $x^2+12x+29=0$  

•  $x^2-12x+43=0$  

•  $x^2+12x-43=0$  

•  $x^2-12x+29=0$