Question

Let ​f(x)=x^2+6x−16​.
Enter the x-intercepts of the quadratic function in the boxes.

Answer 1

`\underline{\underline{\large\bf{Given:-}}}`

`\red{\leadsto}\:`
`\textsf{}`
`\sf f(x)= x^2+6x−16`

`\underline{\underline{\large\bf{To Find:-}}}`

`\orange{\leadsto}\:`
`\textsf{ x-intercepts of the quadratic function }`
`\sf`

`\\`

`\underline{\underline{\large\bf{Solution:-}}}\\`

`\longrightarrow`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.

`\begin{gathered}\\\implies\quad \sf x^2+6x−16=0 \\\end{gathered}`

`\begin{gathered}\\\implies\quad \sf x^2+8x-2x −16=0 \\\end{gathered}`

`\begin{gathered}\\\implies\quad \sf x(x+8)-2(x+8)=0 \\\end{gathered}`

`\begin{gathered}\\\implies\quad \sf (x-2)(x+8)=0\\\end{gathered}`

`\begin{gathered}\\\implies\quad \sf x=2\quad or \quad x=-8 \\\end{gathered}`

`\leadsto`x-intercepts of the given quadratic function are 2 and -8 .