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Suppose that we have an equation y = ax^2 + bx + c whose graph is a parabola with vertex (3,4), vertical axis of symmetry, and contains the point (1,0). What is (a,b,c)?

 Jun 25, 2022
 #1
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If it contains the point (1,0)  then 

 

a + b + c  = 0

 

If the point   (3,4)  is the vertex  than

 

-b/(2a) = 3

-b= 6a

b = -6a

 

Then

 

a(3)^2 + -6a(3) + c  =  4

9a  - 18a + c = 4

-9a + c = 4

c = 4 + 9a

 

So

 

 

a + b + c  = 0

a + ( - 6a)  +  (4 + 9a) =  0

4a =  -4

a = -1

 

b = -6(-1) =  6

 

c =  4 + 9(-1)  =    -5

 

{a , b , c}   = { -1, 6 , - 5 }

 

cool cool cool

 Jun 25, 2022

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