Finding the equations of a graph

I am trying to do a College Algebra project and I am having difficulty findimg the two equations that make the piecewise function in the pictures below.

Letting y be the number of meters the track is above or below the ground
and x the number of meters horizontally from the high point, write the
equation/s expressing y in terms of x for the roller coaster track. The
parabola changes from turning down to turning up at x = 15.

ef47a3b5a9ab85de09af4efe115857fe5g.jpg
 
Last edited:

HallsofIvy

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I am trying to do a College Algebra project by myself as my two partners are not available and I need to find the two equations that make the piecewise function in the pictures below.

Letting y be the number of meters the track is above or below the ground
and x the number of meters horizontally from the high point, write the
equation/s expressing y in terms of x for the roller coaster track. The
parabola changes from turning down to turning up at x = 15.
Are you given that it is a "parabola"? If so your graph can't possibly be right. A parabola is always concave upward or always concave downward.

If, instead, this might be cubic, which is what your graph looks like, then y= [itex]ax^3+ bx^2+ cx+ d[/itex] and putting in four values for x and y gives you four linear equations to solve for a, b, c, d.

 
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It is TWO different parabolas thus a piecewise function, One parabola opening downward and one opening upward. The downward opening parabola ends at (15,12.25) and the upward opening parabola starts at (15,12.25)
 
I believe that the problem is that the graph is badly drawn, If I could find the vertex of the two parabolas I could easily find the leading coefficient and have my equation in a matter of seconds, but the axis arent labeled properly nor is the line very well.
 

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