How do you write the quadratic in vertex form given $y= -2x^2-4x-7$ ?

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Answer 1 · 2015-04-29T08:40:18

The vertex form of a quadratic function is given by
$y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.

We can use the process of Completing the Square to get this into the Vertex Form.

$y=-2x^2-4x-7$

$-> y + 7 = -2x^2 - 4x$ (Transposed -7 to the Left Hand Side)

$-> y + 7 = -2(x^2 + 2x)$ (Made the coefficient of $x^2$ as 1)

Now we subtract $2$ from each side to complete the square

$-> y + 7 - 2 = -2(x^2 + 2x + 1^2)$

$-> y + 5 = -2(x+1)^2$

$-> y + 5 = -2{x-(-1)}^2$

$-> color(green)(y = -2{x - (-1)}^2 + (-5)$ is the Vertex Form

The vertex of the Parabola is ${-1 , -5}$

How do you write the quadratic in vertex form given y= -2x^2-4x-7y= -2x^2-4x-7?