Final answer:
The quadratic equation y = x² +2x - 5 has two x-intercepts. These can be found using the quadratic formula and are confirmed by a positive discriminant.
Step-by-step explanation:
The student has asked about the number of x-intercepts that the equation y = x² +2x - 5 has. The x-intercepts of a quadratic equation can be found by setting y to zero and solving for x. To find the x-intercepts for the given quadratic equation, we set y to 0 and solve the equation 0 = x² + 2x - 5.
Using the quadratic formula, x = (-b ± √(b² - 4ac)) / 2a, where a=1, b=2, and c=-5, we can calculate the values for x. After finding the discriminant (b² - 4ac), which is (2² - 4(1)(-5)) = 4 + 20 = 24, we see that the discriminant is positive, indicating that there are two real solutions for x, and thus the equation has two x-intercepts.