Final answer:
The given equation is a quadratic equation with a vertex at (0, -7) and passes through the point (3, 6). By substituting the coordinates of the vertex and the given point into the equation, we can solve for the coefficients a, b, and c. These values will allow us to write the final equation of the parabola.
Step-by-step explanation:
The given equation is y = ax² + bx + c, with the vertex at (0, -7). This means that the x-coordinate of the vertex is 0, and the y-coordinate is -7. Substituting these values into the equation, we get -7 = a(0)² + b(0) + c, which simplifies to -7 = c. So, the equation becomes y = ax² + bx - 7.
Now, we can use the given point (3, 6) to find the values of a and b. Substituting the coordinates into the equation, we get 6 = a(3)² + b(3) - 7, which simplifies to 6 = 9a + 3b - 7. Rearranging the equation, we have 9a + 3b = 13.
Since we have two equations, -7 = c and 9a + 3b = 13, we can solve them simultaneously to find the values of a, b, and c. This information will allow us to write the final equation of the parabola.