Problem

For the function $y=(x-8)(x+2)$, its $y$-intercept is
its $x$-intercepts are $x=$
Note: If there is more than one $x$-intercept write the $\mathrm{x}$-values separated by commmas.
When $x \rightarrow \infty, y \rightarrow$
$\infty$ (Input + or - for the answer)
When $x \rightarrow-\infty, y \rightarrow$ $\infty$ (Input + or - for the answer)

Answer

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Answer

Final Answer: The y-intercept of the function $y=(x-8)(x+2)$ is \(\boxed{-16}\). The x-intercepts are \(\boxed{-2, 8}\). As $x \rightarrow \infty$, $y \rightarrow \infty$ and as $x \rightarrow -\infty$, $y \rightarrow \infty$.

Steps

Step 1 :The y-intercept of a function is the point where the graph of the function intersects the y-axis. This occurs when x = 0. So, to find the y-intercept, we substitute x = 0 into the function $y=(x-8)(x+2)$, which gives us $y = -16$.

Step 2 :The x-intercepts of a function are the points where the graph of the function intersects the x-axis. This occurs when y = 0. So, to find the x-intercepts, we set the function $y=(x-8)(x+2)$ equal to zero and solve for x, which gives us $x = -2, 8$.

Step 3 :As x approaches infinity, we need to determine the behavior of the function. Since the highest power of x in the function is 2 and the coefficient of x^2 is positive, as x approaches infinity, y will also approach infinity.

Step 4 :Similarly, as x approaches negative infinity, we need to determine the behavior of the function. Since the highest power of x in the function is 2 and the coefficient of x^2 is positive, as x approaches negative infinity, y will also approach positive infinity.

Step 5 :Final Answer: The y-intercept of the function $y=(x-8)(x+2)$ is \(\boxed{-16}\). The x-intercepts are \(\boxed{-2, 8}\). As $x \rightarrow \infty$, $y \rightarrow \infty$ and as $x \rightarrow -\infty$, $y \rightarrow \infty$.

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