Question

Enter Corresponding y

Answer 1

`\begin{cases} f(x)=x^2-2x-15\\\\ f(x)=-x-9 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{they're equal to each other when}}{x^2-2x-15~~ = ~~-x-9}\implies x^2-x-6=0 \\\\\\ (x-3)(x+2)=0\implies x= \begin{cases} 3\\ -2 \end{cases} \\\\[-0.35em] ~\dotfill`

`\stackrel{\textit{substituting on the 1st equation}}{x=3\hspace{5em} f(3)=(3)^2-2(3)-15}\implies f(3)=-12 \\\\\\ \stackrel{\textit{substituting on the 1st equation}}{x=-2\hspace{5em} f(-2)=(-2)^2-2(-2)-15}\implies f(-2)=-7 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} (3~~,~-12)\hspace{5em}(-2~~,~-7) \end{array}}~\hfill`