Question

The graph of f(x) = x2 − 6x − 16 is shown. Which of the following describes all solutions for f(x)?

Answer 1

Answer:

$(x, {x}^{2} - 6x - 16)$ for all real numbers

Step-by-step explanation:

Assuming, the graph continues indefinitely.

The given function is

$f(x) = {x}^{2} - 6x - 16$

To find all solutions to f(x), we equate f(x) to zero.

This implies that:

${x}^{2} - x - 16 = 0$

We factor to obtain:

$(x + 2)(x - 8) = 0$

This gives us;

$x = - 2 \: or \: x = 8$

Hence the graph meets the x-axis at (-2,0) and (8,0).

These are the solutions of f(x), where the graph meets the x-axis.

But the question demands for all solutions.

Therefore $(x, {x}^{2} - 6x - 16)$ for all real numbers is the correct choice