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