Question

Question #9ce6a

Answer 1

`y=-2(x^2+2)-5`

Explanation:

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

Given:`" "y=-2x^2-8x-13`

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

Note that `(-2)xx(+4x)=-8x`

Halve the `x` term

`" "y=-2(x^2+2x)+k-13`

Remove the `x` from the `x` term

`" "y=-2(x^2+2)+k-13`

Move the exponent (power) to outside the brackets.

`" "y=color(red)(-2)(xcolor(magenta)(+2))^2+k-13`

Determine the value of `k`

Set `(color(red)(-2))xx(color(magenta)(+2))^2+k=0`

`=>-8+ k=0" "=>" "k=+8`

`y=-2(x^2+2)+k-13" "->" "y=-2(x^2+2)+8-13`

`y=-2(x^2+2)-5`