Question 16

x = -5 and x = 1

When y = 0 in the equation y = x² + 4x - 5, the values of x that satisfy this equation are -5 and 1, which means the graph intersects the x-axis at these points.

A) x= -5 and x=1

This option is correct because solving the equation x² + 4x - 5 = 0 using factoring or the quadratic formula yields the roots x = -5 and x = 1. These roots represent the x-intercepts of the graph, confirming that y = 0 at these values.

B) x= -2

This option is incorrect because substituting x = -2 into the equation y = x² + 4x - 5 results in y = (-2)² + 4(-2) - 5, which simplifies to y = 4 - 8 - 5 = -9. Therefore, y does not equal 0 when x is -2.

C) x= -5 and x = 0

This option is incorrect because while x = -5 is one of the correct solutions, substituting x = 0 into the original equation gives y = 0² + 4(0) - 5 = -5. Hence, y does not equal 0 at x = 0.

D) x= -9

This option is incorrect as substituting x = -9 into the equation leads to y = (-9)² + 4(-9) - 5, which results in y = 81 - 36 - 5 = 40. Therefore, y does not equal 0 at x = -9.

Conclusion

The correct answer is A) x = -5 and x = 1 because these values are the roots of the equation where y equals 0, indicating the points where the graph intersects the x-axis. All other options fail to satisfy the equation when y is set to 0, thus confirming the validity of option A.