Express $x^2 - 2x - 1$ in the form $(x - a)^2 - b$, where $a$ and $b$ are integers. Hence, F

Question

Express $x^2 - 2x - 1$ in the form $(x - a)^2 - b$, where $a$ and $b$ are integers. Hence, Find the minimum value of $x^2 - 2x - 1$ and the value of $x$ at which the minimum value occurs. Sketch the graph of $y = x^2 - 2x - 1$, stating clearly the turning point, $x$-intercepts and the $y$-intercept.

Accepted Answer

$x^2-2x-1=(x-1)^2-2$, so $a=1$, $b=2$ (a) Minimum $-2$ at $x=1$ (b) Turning point $(1,-2)$; $x$-intercepts $(1-\sqrt2,0)$, $(1+\sqrt2,0)$; $y$-intercept $(0,-1)$

Quadratic Functions, Equations and Inequalities - Completing the Square and Vertex Form

Quadratic Functions, Equations and Inequalities - Completing the Square and Vertex Form

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