A2-9 Quadratic Systems

         Solve Algebraically and Graphically: 
  
(x + )(x + )=0    

x= and x=  

        




     Solve Algebraically and Graphically:  
  

Factored Form:
( x + )(x + ) = 0    

x= and x=  


   

 


A golf pro practices his swing by driving golf balls off the edge of a cliff into a lake. The height of the ball above the lake (measured in meters) as a function of time (measured in seconds and represented by the variable t) from the instant of impact with the golf club is the equation:

Here are the different forms of that equation:
Standard Form:

x-Intercept /Factored Form: 

Vertex Form:

    
Which expression is the most useful for finding how many seconds it takes for the ball to hit the water?
  
                                                                number     units
So when will the ball hit the water?     

Which expression is the most useful for finding the maximum height of the ball?
                  number      units
What is the Max height?    

At what time will it get to that max height?    

What would be the height at 1.1seconds?   

Which equation should you use to find the above answer?  

Use the graph to find the solutions to the equation.  
    
x= , x=   
     Use the graph to find the solutions to the equation

x=  , x=    


         Use the graph to find the solutions to the equation

x= , x=  


         

 
Use the graph to find the solutions to the equation

x= , x=  


         Find the solutions to the equation

x= , x=  



       Use the graph to find the solutions to the equation 

x = , x =   



       Find the solutions to the equation 

x = , x =   




       Use the graph to find the solutions to the equation 
  
x = , x =