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Suppose you are given the function

 

t(x)=x2+8x−20

Explain how you would graph this function, making sure to include the following information:

-coordinate(s) of the solutions/roots

-coordinate of the y-intercept

-location of the line of symmetry

-coordinate of the vertex

-whether the graph opens up or down and how you know

 Apr 8, 2021
 #1
avatar+118626 
+1

y = x^2  + 8x  -  20

 

To  find  the roots  ( x - intercepts)  we  have

 

x^2  + 8x  -  20   = 0   

 

(x + 10)( x - 2)  = 0

 

x +  10  =  0                 x  - 2   =  0 

 

x  = -10                         x  =   2

 

y intercept  =  (0)^2  + 8(0)     -  20     =      -20

 

 

x coordinate  of   vertex  =  -8/ ( 2 * 1)   =   -8 / 2 =    -4

y coordinate of  vertex  =   (-4)^2 + 8 (-4)  - 20  =    16 - 32  - 20  =  -36

equation for  symmetry line    x =  -4

 

This parabola  turns  upward  because  the vertex  at  ( -4, -36)  lies  below  the  y intercept  of  -20

 

(Another  way to tell is that  the  coefficient on x^2 is positive....so ...it  turns upward )

 

 

cool cool cool

 Apr 8, 2021

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