Question

1. complete the table for $x^2 - 4x - 12$.

Explanation:

Step1: Define the given expression

The expression is $f(x) = x^2 - 4x - 12$, where each row uses the same $x$ value for $x$, $x^2$, and $f(x)$.

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Row 1 (given $x=4$):

Step2: Calculate $x^2$

Substitute $x=4$ into $x^2$:
$4^2 = 16$

Step3: Calculate $f(x)$

Substitute $x=4$ into $x^2 - 4x - 12$:
$4^2 - 4(4) - 12 = 16 - 16 - 12 = -12$

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Row 2 (given $x^2=16$):

Step4: Solve for $x$

If $x^2=16$, then $x = \sqrt{16} = 4$ (using the positive root consistent with row 1)

Step5: Calculate $f(x)$

Substitute $x=4$ into $x^2 - 4x - 12$:
$16 - 4(4) - 12 = -12$

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Row 3 (given $f(x)=-12$):

Step6: Solve for $x$

Set $x^2 - 4x - 12 = -12$:
$x^2 - 4x = 0$
$x(x - 4) = 0$
Solutions: $x=0$ or $x=4$. Using $x=4$ (consistent with prior values):

Step7: Calculate $x^2$

Substitute $x=4$ into $x^2$:
$4^2 = 16$

Answer:

$x$	$x^2$	$x^2-4x-12$
4	16	-12
4	16	-12

(Note: If using $x=0$ for the third row, the values would be $x=0$, $x^2=0$, $x^2-4x-12=-12$, but $x=4$ maintains consistency with the provided partial values.)