Additional Mathematics – Quadratic functions | e-Consult
Quadratic functions (1 questions)
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Answer 1
Rewrite the function:
\(f(x)=2\left(x^{2}-4x\right)+5\)
Complete the square inside the parentheses:
\(x^{2}-4x = (x-2)^{2}-4\)
Thus
\(f(x)=2\big[(x-2)^{2}-4\big]+5 = 2(x-2)^{2}-8+5 = 2(x-2)^{2}-3\).
The term \(2(x-2)^{2}\) is always \(\ge 0\). Minimum occurs when \((x-2)^{2}=0\), i.e. \(x=2\).
Minimum value: \(\displaystyle f_{\min}= -3\).