Question

Determine the exact x-intercepts of y=(x+4)^2-7

100 points to whoever gets it right​

Answer 1

`x = -4 + √(7)` and
`x = -4 - √(7)`

Explanation:

The x-intercepts occur at y = 0.

0 = (x + 4)² - 7

x² + 8x + 16 - 7 = 0

x² + 8x + 9 = 0

`x = (-b \pm √(b^2 - 4ac))/(2a)`

`x = (-8 \pm √(8^2 - 4(1)(9)))/(2(1))`

`x = (-8 \pm √(64 - 36))/(2)`

`x = (-8 \pm √(28))/(2)`

`x = (-8 \pm 2√(7))/(2)`

`x = -4 \pm √(7)`

`x = -4 + √(7)` and
`x = -4 - √(7)`

Answer 2

• (- 4 + 7, - 4 - 7)

Explanation:

Given equation:

• y = (x + 4)² - 7

Find its x-intercepts, the values of x when y = 0:

• (x + 4)² - 7 = 0
• (x + 4)² = 7
• x + 4 = ± 7
• x = - 4 ± 7