Given the function:
[tex]y=x^2-2x-8[/tex]The function above is a quadratic function, the graph is a parabola
The standard form of a quadratic function is given by:
[tex]\begin{gathered} ax^2+bx+c=0 \\ \text{for a parabola with }a\text{ vertex (h, k)} \\ If\text{ a<0},\text{ the range is y}\leq k \\ \text{if a>0},\text{ the range is y}\ge k \end{gathered}[/tex]From the given graph and function,
[tex]\begin{gathered} The\text{ vertex (h, k) = (}1,\text{ -9)} \\ a\text{ =1} \\ \sin ce,\text{ a>0, the range is y}\ge-9 \end{gathered}[/tex]Therefore, the range of the function is:
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