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Question #9728b

1 Answer

Mar 30, 2017

$f (x) = - 3 x^{2} - 12 x - 6$ $f(x) = -3x^2 - 12x - 6$

Explanation:

Standard form of a parabola is $f (x) = a x^{2} + b x + c$ $f(x) = ax^2 + bx + c$ .

First, let's distribute out ${(x + 2)}^{2}$ $(x+2)^2$ .

${(x + 2)}^{2}$ $(x+2)^2$

$(x + 2) (x + 2)$ $(x+2)(x+2)$

$(x \cdot x + 2 \cdot x + 2 \cdot x + 2 \cdot 2)$ $(x * x + 2 * x + 2 * x + 2 * 2)$

$x^{2} + 4 x + 4$ $x^2 + 4x + 4$

Now, plug this in to the equation and simplify.

$- 3 {(x + 2)}^{2} + 6$ $-3(x+2)^2 + 6$

$- 3 (x^{2} + 4 x + 4) + 6$ $-3(x^2 + 4x + 4) + 6$

$- 3 x^{2} - 12 x - 12 + 6$ $-3x^2 - 12x - 12 + 6$

$- 3 x^{2} - 12 x - 6$ $-3x^2 - 12x - 6$

Final Answer

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