Given:
Roots:
[tex]\begin{gathered} -3+\sqrt[]{6} \\ -3-\sqrt[]{6} \end{gathered}[/tex]Point: (-1,4)
To determine the equation of the parabola with the given roots and point, we find the missing values first.
Since the roots are given, we can say that the equation is:
[tex]y=a(x+3-\sqrt[]{6})(x+3+\sqrt[]{6})[/tex]Next, we expand the terms.
[tex]y=a(x^2+6x+3)[/tex]Then, we plug in x= -1, and y=4 into the equation to get the value of a.
[tex]\begin{gathered} y=a(x^2+6x+3) \\ 4=a((-1)^2+6(-1)+3) \\ \text{Simplify and rearrange} \\ 4=a(-2) \\ a=\frac{4}{-2} \\ a=-2 \end{gathered}[/tex]So,
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