Answer:
the quadratic function f(x) = -x² - 2x + 3 has two x-intercepts: x = -3 and x = 1.
Explanation:
To find the x-intercepts of the quadratic function f(x) = -x² - 2x + 3, we need to solve the equation f(x) = 0.
Setting -x² - 2x + 3 = 0, we can use the quadratic formula to find the solutions:
x = (-b ± √(b² - 4ac)) / (2a)
For our quadratic equation, a = -1, b = -2, and c = 3.
Substituting these values into the quadratic formula, we get:
x = (-(-2) ± √((-2)² - 4(-1)(3))) / (2(-1))
= (2 ± √(4 + 12)) / (-2)
= (2 ± √16) / (-2)
= (2 ± 4) / (-2)
Now, we have two possible solutions:
1. x = (2 + 4) / (-2) = 6 / (-2) = -3
2. x = (2 - 4) / (-2) = -2 / (-2) = 1