algebra 2 help asap

Question

The path of a roller coaster over a particular length of track can be represented by a quadratic function f, where f(x) represents the vertical displacement above or below a support bar (in meters), and x represents the horizontal displacement to the left or right of a flagpole (in meters). The roller coaster dips below the support bar for values of x between -2 and 1. Which function could represent f ?

Answer 1

Did the question come with any answer choices to choose from? Since it’s specified as being a quadratic you know the general form should be

f(x) = ax^2 + bx + c

Then you can use other criteria given in the question to narrow it down further. For example, you would be looking for a function that meets the criteria where it crosses the x axis at x = -2 and x = 1 since it says that the roller coaster dips below the support bar in between those points. That also means that in between x = -2 and x = 1 the function would need to have a negative value.

I hope that helps get you moving in the right direction on this one! :)