Final answer:
The graphed version of the inequality x² - 4x - 21 > 0 is represented by (x - 7)(x + 3) > 0, which corresponds to option B. The graph shows positive intervals when x is greater than 7 and when x is less than -3. The equation factors into (x - 7)(x + 3) > 0, which corresponds to option B)
Step-by-step explanation:
The graphed version of x² - 4x - 21 > 0 can be found by factoring the quadratic equation. The equation factors into (x - 7)(x + 3) > 0, which corresponds to option B). To determine the graphed version, you would analyze the critical points from the factored form, which are x = 7 and x = -3.
The inequality will be satisfied for x values outside the interval [-3, 7], as this is where the product of the two binomials is positive.
To graph the inequality, plot the critical points on a number line and perform a test point analysis. The graph will show a positive interval to the right of x = 7 and to the left of x = -3.
The equation factors into (x - 7)(x + 3) > 0, which corresponds to option B)