Answer:
[tex]y=\frac{1}{36}\left(x-9\right)^2+7[/tex] is the the equation of parabola that has vertex (9,7) and passes through point (3,8).
Step-by-step explanation:
To solve this you need to use the vertex form of the equation of a parabola which is
[tex]y=a\left(x-h\right)^{2} +k[/tex]
Where (h, k) are the coordinates of the vertex.
So, h = 9 and k =7
And one set of points on the graph
x = 3, y = 8
Solving the formula for [tex]a[/tex].
[tex]y=a\left(x-h\right)^{2} +k[/tex]
[tex]8=a\left(3-9\right)^2+7[/tex]
[tex]\mathrm{Switch\:sides}[/tex]
[tex]a\left(3-9\right)^2+7=8[/tex]
[tex]36a+7=8[/tex]
[tex]36a=1[/tex]
[tex]a=\frac{1}{36}[/tex]
To create a general formula for the parabola you would put in the values for a, h, and k and then simplify.
[tex]y=a\left(x-h\right)^{2} +k[/tex]
[tex]y=\frac{1}{36}\left(x-9\right)^2+7[/tex]
Therefore, [tex]y=\frac{1}{36}\left(x-9\right)^2+7[/tex] is the the equation of parabola that has vertex (9,7) and passes through point (3,8).
The graph is also attached.
Keywords: equation of parabola, vertex, graph
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