Given the general expression of a quadratic function,
[tex]f(x)=ax^2+bx_{}+c[/tex]The given function is,
[tex]f(x)=(x-3)(x+8)[/tex]Expanding the right-hand side of the equation
[tex](x-3)(x+8)[/tex]Apply FOIL method:
[tex]\begin{gathered} \mleft(a+b\mright)\mleft(c+d\mright)=ac+ad+bc+bd \\ \end{gathered}[/tex]Therefore,
[tex]\mleft(x-3\mright)\mleft(x+8\mright)=x\times x+x\times8-3\times x-3\times\: 8=x^2+8x-3x-24[/tex]Simplify
[tex]x^2+8x-3x-24=x^2+5x-24[/tex]Therefore, the function in standard form is
[tex]f(x)=x^2+5x-24[/tex]Now, comparing the general quadratic function and the function given.
[tex]\begin{gathered} ax^2=x^2 \\ \frac{ax^2}{x^2}=\frac{x^2}{x^2} \\ \therefore a=1 \end{gathered}[/tex][tex]\begin{gathered} bx=5x \\ \frac{bx}{x}=\frac{5x}{x} \\ \therefore b=5 \end{gathered}[/tex][tex]c=-24[/tex]Hence, the answers are
[tex]\begin{gathered} a=1 \\ b=5 \\ c=-24 \end{gathered}[/tex]