Express $y=15-4x-4{{x}^{2}}$ in the form $p{{(x+q)}^{2}}+r$ where $p$,$q$ and $r$ are cons

Question

Express $y=15-4x-4{{x}^{2}}$ in the form $p{{(x+q)}^{2}}+r$ where $p$,$q$ and $r$ are constants. State the maximum value of $y$ and the corresponding value of $x$. Sketch the graph of $y=15-4x-4{{x}^{2}}$. Label the coordinates of the turning point and the $x$ and $y$-intercepts on the graph.

Accepted Answer

$y=-4\left(x+\frac12\right)^2+16$, so $p=-4$, $q=\frac12$, $r=16$ (i) Maximum $16$ at $x=-\frac12$ (ii) Turning point $\left(-\frac12,16\right)$; $x$-intercepts $\left(-\frac52,0\right)$, $\left(\frac32,0\right)$; $y$-intercept $(0,15)$

Quadratic Transformations: Completing the Square and Graphing

Quadratic Transformations: Completing the Square and Graphing

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