From the graph shown it can be seen that the bridge is represented by a parabola with vertex of (5, 8) and roots of 1 and 9.
Recall that the vertex form of the equation of a parabola with vertex (h, k) is given by
[tex]y=a(x-h)^2+k[/tex]
Thus, the equation of the given graph in vertex form is given by
[tex]y=a(x-5)^2+8[/tex]
Also, recall that the equation of a parabola with roots, p and q, is given by
[tex]y=a(x-p)(x-q)[/tex]
Thus the equation of the given graph can be given by
[tex]y=a(x-1)(x-9)[/tex]
To get the value of a, we equate both equations and solve as follows:
[tex]a(x-5)^2+8=a(x-1)(x-9) \\ \\ a(x^2-10x+25)+8=a(x^2-10x+9) \\ \\ ax^2-10ax+25a+8=ax^2-10ax+9a \\ \\ 25a-9a=-8 \\ \\ 16a=-8 \\ \\ a=- \frac{8}{16} =- \frac{1}{2} [/tex]
Therefore, the function that Lindsay used to create her design is
[tex]f(x)=-0.5(x-5)^2+8[/tex]
