A curve is such that when y = 0, x = -2 or x = 3. Find the equation of the curve.
A
y = \(x^2 - 5x - 6\)
B
y = \(x^2 + 5x - 6\)
C
y = \(x^2 + x - 6\)
D
y = \(x^2 - x - 6\)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
Since the curve cuts the x-axis at x = -2 and x = 3,
(x + 2)(x - 3) = 0
\(x^2 - 3x + 2x - 6\) = 0
\(x^2 - x - 6\) = 0
Hence, the equation of the curve is
y = \(x^2 - x - 6\)
Source: Myschool Past Questions Archive (Record #49257)