[tex]\underline{\underline{\large\bf{Given:-}}}[/tex]
[tex]\red{\leadsto}\:[/tex][tex]\textsf{} [/tex][tex]\sf f(x)= x^2+6x−16 [/tex]
[tex]\underline{\underline{\large\bf{To Find:-}}}[/tex]
[tex]\orange{\leadsto}\:[/tex][tex]\textsf{ x-intercepts of the quadratic function } [/tex][tex]\sf [/tex]
[tex]\\[/tex]
[tex]\underline{\underline{\large\bf{Solution:-}}}\\[/tex]
[tex]\longrightarrow[/tex]x- intercept is the point where graph of given function touches the x-axis,f(x) becomes 0 at the point where graph of given function touches the x-axis. Therefore, we would to solve x^2+6x−16=0 and find its root.
[tex]\begin{gathered}\\\implies\quad \sf x^2+6x−16=0 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf x^2+8x-2x −16=0 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf x(x+8)-2(x+8)=0 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf (x-2)(x+8)=0\\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf x=2\quad or \quad x=-8 \\\end{gathered} [/tex]
[tex]\leadsto[/tex]x-intercepts of the given quadratic function are 2 and -8 .
