A1D Graphs and x and y intercepts Quad

If you have not watched the video, here is the video to watch to help you on this assignment.  There are headphones in the closet.  If you take class time to watch the video, you will need to finish the rest of the assignment at home that you don't complete in class. 


Excellent work, Decoders! You've mastered the ancient language. Now, a new discovery has been made at the dig site: a set of shattered stone tablets.

Legend says that when the fragments are correctly reassembled, they form a map leading to a greater prize—an ancient and powerful artifact. Your next mission is to work with your expedition teams to match these 'Ancient Tablet Fragments' and find the location of the Cipher Disk! 



Complete the following table:  Here is the link for the shattered Stone tablet  (matching cards) if you missed class. 
https://docs.google.com/document/d/1EabOMlaFN83qjuyZfbi7E0PRPWPft38RnWd9WilL3YI/edit?usp=sharing

   
GRAPHFactored or x-intercept EQUATIONX-intercept(s)y-interceptsCHECK
A    
 y = (x+5)(x-3) 
  (-2,0) (7,0) 
   (0,21)
E   
  (5,0) 
 y= (x+3)(x+5)  
G   
  (5/2,0) (-7,0) 

Success! Your teams have reassembled the map fragments, and they've led us right to it... The legendary Archaeologist's Cipher Disk.

The artifact is dormant, its secrets locked away. Each quadratic you solve from here on out will provide the key to align one more ring. Let's begin the decoding sequence!


The Artifact is Found: "Deep within the dusty ruins of a forgotten civilization near Lehi, Utah, your team unearths an ancient stone disk covered in cryptic symbols. Its secrets are locked, waiting for a brilliant mind to decipher them.









     
Given the Factored Form:      

x-Intercepts  (, ) (  , )
    

y-intercepts:  ( , )
 

End Behavior:  Left Side           Right Side 
  
The First Ring Aligns: "Your knowledge of quadratic intercepts unlocks the mechanism of the outermost ring. A few symbols glow, hinting that the path to the treasure has begun to illuminate.
Graph the Intercepts with dots:  
Use Double Translate Arrows until the graph until it matches the x and y -intercepts.  




     
Given the Factored Form:      

x-Intercepts  (, ) (  , )
    

y-intercepts:  ( , )
 

End Behavior:  Left Side           Right Side 
  

The Second Ring Clicks: "With the next layer of the code deciphered, the second ring snaps into place. The light intensifies, revealing more of the ancient language and deepening the mystery.
HEERHERHEHRHERHE
HERHHRHERHEHH
Graph the Intercepts with dots:  
Use Double Translate Arrows until the graph until it matches the x and y -intercepts.  



p : 3  
Given the equation , find the following.

x-Intercepts:  (, )   (, )

y-Intercept:  ( , )

       

End Behavior:  

Left Side               Right Side:  
  

The Third Ring Aligns: "Another set of intercepts solved, another ring clicks! The artifact hums with a growing energy, as if the secrets within are stirring

HEHREHRHERHERH
Graph the above graph.  Use the singe arrow for small increments if needed.

Given the equation , find the following.

x-Intercepts:  (, )   (, )

y-Intercept:  ( , )

       

End Behavior:  

Left Side               Right Side:  
  

 
Halfway There: "You're halfway through the puzzle! The light from the aligned rings begins to touch the dormant core, a sign that the heart of the cipher is awakening.



       
Given the Equation     find the following: 

y-Intercept (BE CAREFUL.  Remember the rule. )    (, )

x-Intercept:   (, )   ( ,  ) 

        


End Behavior:

Left Side:                  Right Side 
  

The Final Ring Aligns: "With a final surge of mathematical prowess, the last ring slides into its correct position. A powerful energy now flows into the central symbol, ready to reveal its truth.
Graph:    
Check Intercepts that are on graph   


x-intercepts:  (, )  (,  )
  
y-intercept:  (, )
 
Factored Form:  y = 

Double Distribute to get STANDARD FORM:  
y =   x + 
   
End Behavior:   Left side:   Right side: 
 

The Core Awakens: "The heart of the cipher pulses with light! The ancient energy, dormant for centuries, is now fully awakened by your students' sharp minds."
 
Find the information below for this graph if the scale factor is 1.

HEHRHEHREHFind the x and y -intercepts, and then sketch a graph.         
 If there are not 2, leave the extra boxes blank.. 
x-Intercept(s):  (, ) (, )    

y-Intercept(s):  (, )  (, )    

HEHREHREH
The Beam of Light: "A focused beam of pure light erupts from the center of the disk! The artifact is no longer a mystery, but a key, searching for the hidden location."

Graph:    



     
Given the Equation     find the following: 

y-Intercept (BE CAREFUL.  Remember the rule. )    (, )

x-Intercept:   (, )   ( ,  ) 

        


End Behavior:

Left Side:                  Right Side 
  

 
   


The Map is Revealed: "The beam of light strikes the air above the disk, projecting a ghostly image of a long-lost treasure map! The parabola's path has led you to this very moment."
Find the x and y -intercepts, and then sketch a graph.         
 If there are not 2, leave the extra boxes blank.. 
x-Intercept(s):  (, ) (, )    

y-Intercept(s):  (, )  (, )    


The Treasure Map is Uncovered!: "The light from the fully activated cipher disk now shines upon a hidden scroll, revealing the final 'X' that marks the treasure!  Congratulations, Quadratic Archaeologists, you've found it!"


Graph: