The graph of the equation y = x² + 4x - 5 is shown on the grid. Which statement is true when y = 0?

Rationale

x = -5 and x = 1.

To find the values of x when y = 0 in the equation y = x² + 4x - 5, we set the equation equal to zero and factor it. The resulting factored form (x + 5)(x - 1) = 0 shows that the solutions are x = -5 and x = 1.

A (x= -5 and x=1) CORRECT

This choice correctly identifies the solutions to the equation when y = 0. By factoring the quadratic equation, we find that setting y to zero gives us the two x-values, -5 and 1, which satisfy the equation.

B (x= -2) YOUR ANSWER

This choice is incorrect because substituting x = -2 into the equation y = x² + 4x - 5 does not yield zero. Instead, it results in y = (-2)² + 4(-2) - 5 = 4 - 8 - 5 = -9, which is not equal to zero.

C (x= -5 and x = 0) YOUR ANSWER

This choice is incorrect because, while -5 is one of the solutions, x = 0 does not satisfy the equation. Substituting x = 0 results in y = 0² + 4(0) - 5 = -5, which is also not equal to zero.

D (x= -9) YOUR ANSWER

This choice is incorrect as substituting x = -9 into the equation results in y = (-9)² + 4(-9) - 5 = 81 - 36 - 5 = 40, which does not equal zero.

Conclusion

The correct solutions to the equation y = x² + 4x - 5 when y = 0 are indeed x = -5 and x = 1, as confirmed by the factorization of the quadratic. Choices B, C, and D do not satisfy the condition y = 0, emphasizing the importance of verifying solutions in quadratic equations.

The graph of the equation y = x² + 4x - 5 is shown on the grid. Which statement is true when y = 0?

x = -5 and x = 1.

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