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avatar+279 

I think this one is easy, but I sorta forgot how to get equations from graphs and all the equations and jazz ):

A parabola with equation y=x^2+bx+c passes through the points (-1, -11) and (3, 17). What is c?

 May 30, 2019
 #1
avatar+8873 
+4

y  =  x2 + bx + c

 

The graph of the equation passes through the point  (-1, -11)  so we know....

 

-11  =  (-1)2 + b(-1) + c

 

-11  =  1 - b + c

                                 Add  b  to both sides.

-11 + b  =  1 + c

                                 Add  11  to both sides.

b  =  12 + c

 

The graph of the equation passes through the point  (3, 17)  so we know....

 

17  =  (3)2 + b(3) + c

 

17  =  9 + 3b + c

                                 Subtract  9  from both sides.

8  =  3b + c

                                 And we know  b  =  12 + c  so we can substitute  12 + c  in for  b .

8  =  3(12 + c) + c

                                 Distribute  3  to the terms in parenthesees.

8  =  36 + 3c + c

                                 Subtract  36  from both sides.

8 - 36  =  3c + c

                                 Combine like terms.

-28  =  4c

                                 Divide both sides by  4 .

-7  =  c

 

Check: https://www.desmos.com/calculator/pu7pbnc9br

 May 30, 2019
 #2
avatar+279 
+2

Thanks for your help! :)

 May 30, 2019

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