Express $y=4{{x}^{2}}-8x-5$ in the form $y=a{{(x-h)}^{2}}+k$, where $a$, $h$ and $k$ are c

Question

Express $y=4{{x}^{2}}-8x-5$ in the form $y=a{{(x-h)}^{2}}+k$, where $a$, $h$ and $k$ are constants. Hence, state Find the maximum or minimum value of the graph The value of $x$ at which the maximum or minimum occurs Hence, sketch the curve for $y=4{{x}^{2}}-8x-5$, indicating clearly the turning points and intercepts on the axes.

Accepted Answer

$y=4(x-1)^2-9$ (i) Minimum $-9$ (ii) $x=1$ (iii) $x=-\frac12,\frac52$; $y$-intercept $(0,-5)$

Completing the Square when \(a\ne 1\)

Completing the Square when \(a\ne 1\)

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