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Find constants a, h, k such that 3x^2 + 4x + 1 = a(x - h)^2 + k.

 Jun 21, 2022
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3x^2  + 4x  +  1  =  a( x + h)^2 + k

 

3x^2 + 4x + 1  =  a (x^2 + 2xh + h^2) + k

 

3x^2 + 4x + 1  =  ax^2 + 2ahx + ah^2  + k

 

a = 3

 

4  = 2ah

4 = 2(3)h

4 = 6h

h = 4/6 = 2/3

 

ah^2 + k =  1

3(2/3)^2 + k  = 1

(4/3) + k =  1

 

k =  1  - 4/3

k = -1/3

 

 

cool cool cool

 Jun 21, 2022

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