Express ${{x}^{2}}-2x-5$ in the form of ${{\left( x+a \right)}^{2}}+b$. Sketch the graph of \(y=

Question

Express ${{x}^{2}}-2x-5$ in the form of ${{\left( x+a \right)}^{2}}+b$. Sketch the graph of $y={{x}^{2}}-2x-5$ on the axes below. Indicate clearly the values where the graph crosses $y$-axes and the turning point.

Accepted Answer

(i) $x^2-2x-5=(x-1)^2-6$. (ii) Turning point: $(1,-6)$; $y$-intercept: $(0,-5)$; $x$-intercepts: $(1-\sqrt6,0)$ and $(1+\sqrt6,0)$.

Completing the Square and Sketching a Quadratic Graph

Completing the Square and Sketching a Quadratic Graph

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