Final Answer:
The equation for a parabola with a vertex at (0, 6) that goes through the point (2, 7) can be expressed in the form y = ax^2 + bx + c. The specific equation is y = 0.5x^2 + 6.
Step-by-step explanation:
The general form of a quadratic equation (parabola) is y = ax^2 + bx + c, where (h, k) represents the vertex. In this case, the vertex is given as (0, 6). The vertex form of the equation is y = a(x - h)^2 + k. Substituting the given vertex coordinates yields y = a(x - 0)^2 + 6, which simplifies to y = ax^2 + 6.
Now, to find the value of 'a,' you can use the fact that the parabola passes through the point (2, 7). Substitute these coordinates into the equation: 7 = a(2)^2 + 6. Solving for 'a,' you get a = 0.5.
Therefore, the equation for the parabola is y = 0.5x^2 + 6. This equation represents a parabola with a vertex at (0, 6) and passes through the point (2, 7).