Question

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

a parabola passing through negative 2 comma zero, 0 comma negative 16, and 8 comma zero

(−2, 0), (0, −16), (3, −25), (8, 0)
(x, x2 − 6x − 16) for all real numbers
(−2, 0), (8, 0)
(x, y) for all real numbers

Answer 1

(x, x^2 − 6x − 16) for all real numbers

Explanation:

look above, also

A doesnt make sense

C doesnt make sense

D it is not y it is x^2 − 6x − 16

B is right

Answer 2

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

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