Question

use a graph to solve the inequality:
$x^2 - x - 12 > 0$
to solve the inequality, identify the values of $x$ that make the value of the expression $x^2 - x - 12$ greater than 0.
graph the equation $y = x^2 - x - 12$ by plotting points. complete the following table.

$x$	$-2$	$-1$	$0$	$1$	$2$
$x^2 - x - 12$	$-6$	$-10$	$-12$	$-12$	$-10$

use the points to sketch the right.
to solve the inequality, the value of the function is dropdown
positive or 0, negative, negative or 0 where the...

Explanation:

Step1: Analyze the function type

The function \( y = x^2 - x - 12 \) is a quadratic function, so its graph is a parabola. The coefficient of \( x^2 \) is positive (\( a = 1>0 \)), so the parabola opens upwards.

Step2: Find the roots (x-intercepts)

To find where \( y = 0 \), solve \( x^2 - x - 12 = 0 \). Factor the quadratic: \( x^2 - x - 12=(x - 4)(x + 3)=0 \). So the roots are \( x = 4 \) and \( x=-3 \).

Step3: Analyze the inequality \( x^2 - x - 12>0 \)

For a parabola opening upwards, the function is positive (above the x - axis) when \( x < - 3 \) or \( x>4 \), because the parabola is above the x - axis outside the interval between its two roots. We can also check the sign of the function using the table values. For example, when \( x=-4 \) (not in the table, but we can calculate \( y=(-4)^2-(-4)-12 = 16 + 4-12 = 8>0 \)), when \( x = 5 \), \( y = 5^2-5 - 12=25 - 5 - 12 = 8>0 \), and between \( - 3 \) and \( 4 \) (e.g., \( x = 0 \), \( y=-12<0 \)), which confirms the solution.

Answer:

The solution to the inequality \( x^2 - x - 12>0 \) is \( x < - 3 \) or \( x>4 \)