Final answer:
To write the equation for a parabola with vertex at (-3, 12) and passing through the point (0, 6), we can use the vertex form of a quadratic equation: y = a(x-h)^2 + k. The equation for the parabola is y = (-2/3)(x + 3)^2 + 12.
Step-by-step explanation:
To write the equation for a parabola with vertex at (-3, 12) and passing through the point (0, 6), we can use the vertex form of a quadratic equation: y = a(x-h)^2 + k. In this equation, (h, k) represents the vertex.
Plugging in the given vertex coordinates, we have y = a(x - (-3))^2 + 12. Simplifying further, y = a(x + 3)^2 + 12.
To find the value of 'a,' we can substitute the coordinates of the point (0, 6): 6 = a(0 + 3)^2 + 12. Solving for 'a,' 6 = 9a + 12. Subtracting 12 from both sides, we get -6 = 9a. Dividing by 9, we find that a = -2/3.
Therefore, the equation for the parabola is y = (-2/3)(x + 3)^2 + 12.