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The equation is y = 2x2 - 3x.

You are watching: Y=-2x-2

Here x2coefficient is 2, because that perfect square do x2coefficient 1 by factor out 2.

y = 2(x2 - 3/2 x )

To readjust the expression (x2 - 3/2 x ) into a perfect square trinomialadd (half thexcoefficient)²to every side that the expression.

Herexcoefficient = 3/2. So, (half thexcoefficient)² = (3/4)2= 9/16.

Add 2(9/16) = 9/8 to each side of the equation.

y + 9/8 = 2(x2 - 3/2 x + 9/16)

y + 9/8 = 2(x - 3/4)2

y = 2(x - 3/4)2 - 9/8

The above equation represent the standard type of the equation the parabola.

The standard kind of the parabola with vertex (h, k) and axis of the opposite x = h is y = a(x - h)2 + k.

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The vertex kind of the equation that parabola is y = 2(x - 3/4)2 - 9/8 and also Vertex : (h, k ) = (3/4, - 9/8).