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The quadratic equation that best represents his model of the relationship between stock value and time is given by:
[tex]y = -0.0976(x - 10)^2 + 18, x \geq 0[/tex]
The graph is given at the end of the answer.
The equation of a quadratic function, of vertex (h,k), is given by:
[tex]y = a(x - h)^2 + k[/tex]
In which a is the leading coefficient.
In this problem, the maximum value was a share value of $18 after 10 days, hence the vertex is:
(h,k) = (10,18).
Thus:
[tex]y = a(x - 10)^2 + 18[/tex]
Since the initial price was of $8 per share, we have that:
[tex]8 = a(0 - 10)^2 + 18[/tex]
[tex]-82a = 8[/tex]
[tex]a = -\frac{8}{82}[/tex]
[tex]a = -0.0976[/tex]
Hence the equation is:
[tex]y = -0.0976(x - 10)^2 + 18, x \geq 0[/tex]
At the end of the answer, the sketch of the graph is given.
More can be learned about quadratic equations at https://brainly.com/question/24737967
