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Rewrite the function f(x)=3(x-4)^(2)+2 in the form f(x)=ax^(2)+bx+c. f(x)=

Rewrite the function f(x)=3(x−4)2+2 f(x)=3(x-4)^{2}+2 in the form f(x)=ax2+bx+c f(x)=a x^{2}+b x+c .\newlinef(x)= f(x)=

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Q. Rewrite the function f(x)=3(x−4)2+2 f(x)=3(x-4)^{2}+2 in the form f(x)=ax2+bx+c f(x)=a x^{2}+b x+c .\newlinef(x)= f(x)=
  1. Expand Squared Term: Expand the squared term using the formula (a−b)2=a2−2ab+b2(a-b)^2 = a^2 - 2ab + b^2.\newlineCalculation: (x−4)2=x2−8x+16(x-4)^2 = x^2 - 8x + 16.
  2. Multiply Expanded Form: Multiply the expanded form by 33.\newlineCalculation: 3(x2−8x+16)=3x2−24x+483(x^2 - 8x + 16) = 3x^2 - 24x + 48.
  3. Add Constant Term: Add the constant term from the original function.\newlineCalculation: 3x2−24x+48+2=3x2−24x+503x^2 - 24x + 48 + 2 = 3x^2 - 24x + 50.

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