Equation of the parabola with the vertex (0,3), axis parallel to OX, passing through (4,9)
x = a(y-3)^2 + 0
but (4,9) lies on it, so
4 = a(9-3)^2 + 0
4 = 36a
a = 1/9
x = (1/9)(y-3)^2 is your equation.
To find the equation of the parabola with the given information, we need to 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.
From the given information, we know that the vertex is (0, 3), so we can substitute these values into the equation:
y = a(x - 0)^2 + 3
y = ax^2 + 3
Now we need to find the value of 'a' in order to complete the equation. We can do this by using the fact that the parabola passes through the point (4, 9):
Substituting (x, y) = (4, 9) into the equation, we get:
9 = a(4)^2 + 3
9 = 16a + 3
6 = 16a
a = 6/16
a = 3/8
Now we have the value of 'a', we can substitute it back into our equation:
y = (3/8)x^2 + 3
Therefore, the equation of the parabola with the vertex (0,3), axis parallel to OX, and passing through (4,9) is y = (3/8)x^2 + 3.