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Answer 1 · 2017-05-29T11:50:52

$y = - 2 (x^{2} + 2) - 5$ $y=-2(x^2+2)-5$

See https://socratic.org/s/aF6V8h4L for another full explanation of method but with a different equation.

Given: $y = - 2 x^{2} - 8 x - 13$ $" "y=-2x^2-8x-13$

Write as: $y = - 2 (x^{2} + 4 x) + k - 13$ $" "y=-2(x^2+4x)+k-13$

Note that $(- 2) \times (+ 4 x) = - 8 x$ $(-2)xx(+4x)=-8x$

Halve the $x$ $x$ term

$y = - 2 (x^{2} + 2 x) + k - 13$ $" "y=-2(x^2+2x)+k-13$

Remove the $x$ $x$ from the $x$ $x$ term

$y = - 2 (x^{2} + 2) + k - 13$ $" "y=-2(x^2+2)+k-13$

Move the exponent (power) to outside the brackets.

$y = - 2 {(x + 2)}^{2} + k - 13$ $" "y=color(red)(-2)(xcolor(magenta)(+2))^2+k-13$

Determine the value of $k$ $k$

Set $(- 2) \times {(+ 2)}^{2} + k = 0$ $(color(red)(-2))xx(color(magenta)(+2))^2+k=0$

$\Rightarrow - 8 + k = 0 \Rightarrow k = + 8$ $=>-8+ k=0" "=>" "k=+8$

$y = - 2 (x^{2} + 2) + k - 13 \to y = - 2 (x^{2} + 2) + 8 - 13$ $y=-2(x^2+2)+k-13" "->" "y=-2(x^2+2)+8-13$

$y = - 2 (x^{2} + 2) - 5$ $y=-2(x^2+2)-5$

Tony B