Final answer:
The equation of the parabola in vertex form, given the vertex (0,7) and the point (1, -2), is y = -9x² + 7.
Step-by-step explanation:
To write the equation of the parabola in vertex form, given the vertex (0,7) and a point (1, -2), we will use the vertex form of a parabola, which is y = a(x - h)² + k, where (h, k) is the vertex of the parabola. Since the vertex is (0,7), our equation will be y = a(x - 0)² + 7 or y = ax² + 7. We can find the value of 'a' by plugging in the coordinates of the given point (1, -2).
Substitute the point (1, -2) into the equation: -2 = a(1)² + 7. Simplify to -2 = a + 7, and then solve for 'a' which gives a = -9. Now we substitute 'a' back into the original equation to get the final vertex form of the parabola: y = -9x² + 7.