Determine the x-intercept of the quadratic function:

y=-0.25 (x+1) ^2+9

Y = ⁻¹/₄ (x + 1) ² + 9

0 = ⁻¹/₄ (x + 1) ² + 9

0 = ⁻¹/₄ (x + 1) (x + 1) + 9

0 = ⁻¹/₄ (x (x + 1) + 1 (x + 1)) + 9

0 = ⁻¹/₄ (x (x) + x (1) + 1 (x) + 1 (1)) + 9

0 = ⁻¹/₄ (x² + x + x + 1) + 9

0 = ⁻¹/₄ (x² + 2x + 1) + 9

0 = ⁻¹/₄ (x²) - ¹/₄ (2x) - ¹/₄ (1) + 9

0 = ⁻¹/₄x² - ¹/₂x - ¹/₄ + 9

0 = ⁻¹/₄x² - ¹/₂x + 8³/₄

x = - (⁻¹/₂) ± √ ((⁻¹/₂) ² - 4 (⁻¹/₄) (8³/₄))

2 (⁻¹/₄)

x = ¹/₂ ± √ (¹/₄ + 8³/₄)

⁻¹/₂

x = ¹/₂ ± √ (9)

⁻¹/₂

x = ¹/₂ ± 3

⁻¹/₂

x = ¹/₂ + 3 U x = ¹/₂ - 3

⁻¹/₂ ⁻¹/₂

x = 4 U x = - 2¹/₂

⁻¹/₂ ⁻¹/₂

x = - 8 U x = 5