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{3}{50}(x - 3)^2 + 2[/tex]
Given that:
[tex](h,k) = (3,2)[/tex] -- vertex
[tex](x,y) = (13,8)[/tex] --- the point
Recall that:
[tex]y = a(x - h)^2 + k[/tex]
Substitute [tex](h,k) = (3,2)[/tex] in [tex]y = a(x - h)^2 + k[/tex]
[tex]y = a(x - 3)^2 + 2[/tex]
Substitute [tex](x,y) = (13,8)[/tex] in [tex]y = a(x - 3)^2 + 2[/tex]
[tex]8 = a(13 - 3)^2 + 2[/tex]
[tex]8 = a(10)^2 + 2[/tex]
Collect like terms
[tex]a(10)^2 = 8 - 2[/tex]
[tex]a(10)^2 = 6[/tex]
Make a the subject
[tex]a= \frac{6}{10^2}[/tex]
[tex]a= \frac{6}{100}[/tex]
[tex]a= \frac{3}{50}[/tex]
Hence, the equation of the parabola is:
[tex]y = \frac{3}{50}(x - 3)^2 + 2[/tex]
See attachment for the graph of [tex]y = \frac{3}{50}(x - 3)^2 + 2[/tex]
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