The points (3, 8) and (6, 8) are part of the solution set of a quadratic inequality, while (5, 9) and (7, 7) are not. The point that must also be part of the solution set is
A. (4, 7)
B. (4, 9)
C. (8, 6)
D. (6, 10)
C???
To determine which point must also be part of the solution set of the quadratic inequality, let's start by understanding the given information. We have two points that are part of the solution set: (3, 8) and (6, 8), and two points that are not part of the solution set: (5, 9) and (7, 7).
Since the y-coordinate of the points (3, 8) and (6, 8) is the same for both, it indicates that the quadratic inequality has a horizontal line as its solution. This means that the quadratic inequality will have an equation of the form y = k, where k is the y-coordinate of the points (3, 8) and (6, 8).
So, the equation of the quadratic inequality is y = 8.
To find the point that must also be part of the solution set, we need to substitute the x-coordinate of each answer choice into the equation y = 8 and see which one satisfies it.
Let's substitute the x-coordinate of each answer choice into the equation y = 8:
A. (4, 7): Substitute x = 4 into y = 8: y = 8 which is not equal to 7. So, (4, 7) is not part of the solution set.
B. (4, 9): Substitute x = 4 into y = 8: y = 8 which is not equal to 9. So, (4, 9) is not part of the solution set.
C. (8, 6): Substitute x = 8 into y = 8: y = 8 which is not equal to 6. So, (8, 6) is not part of the solution set.
D. (6, 10): Substitute x = 6 into y = 8: y = 8 which is not equal to 10. So, (6, 10) is not part of the solution set.
From the calculations, we can see that none of the answer choices satisfy the equation y = 8. Therefore, none of the given points must also be part of the solution set.