Create an unique parabola in the pattern of f(x) = ax2 + bx + c.

Hi, really need help with this Algebra problem.

Ray needs help creating the second part of the coaster. Create an unique parabola in the pattern of f(x) = ax2 + bx + c. Describe the direction of the parabola and determine the y-intercept and zeros.

The safety inspector notes that Ray also needs to plan for a vertical ladder through the centre of the coaster's parabolic shape for access to the coaster to perform safety repairs. Find the vertex and the equation for the axis of symmetry of the parabola, showing your work, so Ray can include it in his coaster plan.

Thank you so much!