Question

Your job is to design the 2nd part of the roller coaster by creating a unique parabola in the form: h(x)=ax^2+bx+c. knowing there are safety requirements which needs to be met, a vertical ladder through the center of the 2nd section's parabolic shape for access to the roller coaster must be part of the design. find the vertex and the equation for the axis of symmetry of the parabolic section.

Answer 1

To design a parabolic section of a roller coaster, one can find the vertex of the parabola h(x) = ax^2 + bx + c using the vertex formula and then determine the axis of symmetry, which is critical for safety and design.

Step-by-step explanation:

The question concerns the design of the second part of a roller coaster and involves finding the vertex and the equation for the axis of symmetry of a parabola represented by h(x) = ax2 + bx + c. The vertex of a parabola in this form can be found using the formula -b/(2a) for the x-coordinate, and then substituting this back into the equation to find the y-coordinate of the vertex. The axis of symmetry can be represented by the equation x = -b/(2a). In designing a coaster, these elements are crucial for ensuring the safety and proper functioning of the ride.

To illustrate, if a parabola is given by h(x) = 2x2 - 4x + 6, the vertex can be calculated as follows: The x-coordinate of the vertex is -(-4)/(2*2) = 1, and substituting x = 1 into h(x) gives us the y-coordinate: h(1) = 2(1)2 - 4(1) + 6 = 4. Therefore, the vertex is at (1, 4), and the axis of symmetry is the line x = 1.