A mirror with a parabolic cross section is used to collect sunlight on a pipe located at the focus of the mirror. The pipe is located 9 inches from the vertex of the mirror. Write an equation of the parabola that models the cross section of the mirror. Assume that the parabola opens upward. (1 point)
Since the parabola opens upward and the pipe is located at the focus of the mirror, the vertex of the parabola is also the focus of the parabola. The equation of a parabola with vertex (h, k) that opens upward is given by the equation y = a(x - h)^2 + k, where a is a positive constant.
In this case, the vertex is located at (h, k) = (0, 0) since the parabola opens upward. The pipe is located 9 inches from the vertex, so its position can be represented by the x-coordinate -9.
Plugging these values into the equation, we have y = a(x - 0)^2 + 0.
Simplifying, we get y = ax^2.
Therefore, the equation of the parabola that models the cross section of the mirror is y = ax^2.