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Quadratic Functions, Equations and Inequalities - Solving Quadratic Equations by Completing the Square

Quadratic Functions, Equations and Inequalities - Solving Quadratic Equations by Completing the Square

Secondary 3

Express \(\mathrm{f}\left( x \right)=-{{x}^{2}}-x+1\) in the form of \(f(x)=-{{(x-h)}^{2}}+k\). Hence, solve \(\mathrm{f}\left( x \right)=0\).

Solution:

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Answer:\(f(x)=-\left(x+\dfrac12\right)^2+\dfrac54\), so \(h=-\dfrac12,\;k=\dfrac54\). Roots: \(x=\dfrac{-1\pm\sqrt5}{2}\).

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