the function h(x)=1/98x^2 describes h(x), the height of part of a roller coaster track, where x is the horizontal distance in feet from the center of this section of the track. The towers that support this part of the track are the same height and are 150 feet apart. which is the best estimate of the height of the towers?

obviously x goes from -75 to +75

So, 1/98 * 75^2 = 57.4 feet high

To find the best estimate of the height of the towers, we can utilize the given function h(x) = (1/98)x^2, which describes the height of the roller coaster track as a function of the horizontal distance x from the center of the section of the track. The towers are located 150 feet apart from each other.

Since the function is quadratic, it means that the height of the track increases as x gets farther from the center. To find the height of the towers, we need to determine the highest point on the track. The highest point corresponds to the vertex of the quadratic function.

The formula for the x-coordinate (horizontal location) of the vertex of a quadratic function in the form y = ax^2 + bx + c is given by x = -b / (2a). In our case, the equation is h(x) = (1/98)x^2, so a = 1/98 and b = 0. Plugging these values into the formula, we get:

x = -0 / (2 * 1/98)
= -0 / (2/98)
= -0 / (1/49)
= 0

Therefore, the x-coordinate of the vertex is x = 0. Since the towers are located 150 feet apart from each other, the center of the section of the track is at x = 0, and thus the highest point or vertex also corresponds to the center.

From the equation h(x) = (1/98)x^2, we can substitute x = 0 to find the height at the vertex:

h(0) = (1/98)(0)^2
= 0

Hence, the height of the towers is approximately 0 feet, which means they are at ground level or close to it.