Answer:
Explanation:
To find the x-intercepts of a quadratic function, we set y = 0 and solve for x. So, for the given function:
-1/2x^2 + x + 5/2 = 0
Multiplying both sides by -2 to eliminate the fraction:
x^2 - 2x - 5 = 0
We can solve for x using the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 1, b = -2, and c = -5:
x = (2 ± sqrt(4 + 20)) / 2
x = (2 ± 2sqrt(6)) / 2
x = 1 ± sqrt(6)
Therefore, the x-intercepts of the quadratic function y = -1/2x^2 + x + 5/2 are
x = 1 + sqrt(6)
and
x = 1 - sqrt(6).