The equation of a parabola is: [tex]y = a(x - h)^2 + k[/tex] where (h,k) represents the vertex.
The equation of the parabola is: [tex]y = \frac{18}{625}(x - 25)^2 + 90[/tex]
We have:
[tex](h,k) = (25,90)[/tex] --- the vertex
[tex](x,y) = (50,0)[/tex] -- one of its point.
Recall that:
[tex]y = a(x - h)^2 + k[/tex]
Substitute [tex](h,k) = (25,90)[/tex]
[tex]y = a(x - 25)^2 + 90[/tex]
To solve for a, we substitute [tex](x,y) = (50,0)[/tex]
[tex]0 = a(50 - 25)^2 + 90[/tex]
[tex]0 = a(25)^2 + 90[/tex]
Collect like terms
[tex]a(25)^2 = 90[/tex]
[tex]625a = 90[/tex]
Solve for a
[tex]a = \frac{90}{625}[/tex]
[tex]a = \frac{18}{125}[/tex]
Recall that:
[tex]y = a(x - 25)^2 + 90[/tex]
Hence, the equation of the parabola is:
[tex]y = \frac{18}{625}(x - 25)^2 + 90[/tex]
See attachment for the graph of [tex]y = \frac{18}{625}(x - 25)^2 + 90[/tex]
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