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