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Write the equation of the parabola with the vertex (2, -4) that goes through the origin

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To write the equation of a parabola with the vertex (2, -4) that goes through the origin, we can use the standard form of the equation for a parabola:

y = a(x - h)^2 + k

Where (h, k) represents the vertex of the parabola.

Given that the vertex is (2, -4), we can substitute these values into the equation:

y = a(x - 2)^2 - 4

Since the parabola also goes through the origin, we can substitute (0, 0) into the equation:

0 = a(0 - 2)^2 - 4

Simplifying this equation gives us:

0 = 4a - 4

To isolate 'a', we can add 4 to both sides:

4 = 4a

Dividing both sides by 4:

1 = a

Therefore, the equation of the parabola is:

y = (x - 2)^2 - 4
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