Find the x-intercepts for the quadratic function y= -1/2(x+3)^2 +4

x= -3 +√2 ≈ -0.1716,  and x = - 3 -2√2 ≈ -5.8284

Step-by-step explanation:

y= -1/2(x+3)² +4

For x -intercept, y = 0.

0 = - 1/2(x+3)² + 4 /*(-2)

0 = (x+3)² - 8

(x+3)² = 8

√(x+3)² = +/-√8

x+3 = +/-√8

x = - 3+/- 2√2

x= -3 +√2 ≈ -0.1716,  and x = - 3-2√2 ≈ -5.8284