Question

1. Explain why the equation (x-4)² - 288 has two solutions. Then solve the equation to find the solutions.

Show your work.
Answer:

Answer 1

x =12√2 + 4 and x = 12√2 - 4

Explanation:

the reason why it has two solutions is that the vertex is at (4, -288). this is a positive quadratic equation. the vertex is below the x-axis, so the graph will meet the x-axis twice.

to solve it, (x - 4)² - 288 = 0

(x - 4)² = 288

(x - 4) = ±√288

x = ±√288 + 4

= 12√2 ± 4