Question:
Which of the equivalent expressions for P(x) reveals the profit when the price is
zero without changing the form of the expression? P(x) = -3x² + 432x - 1680
a) P(x) = -3(x - 4)(x - 140)
b) P(x) = -3(x - 72)² + 13872
Find the profit when the price is zero
Answer:
- P(x) = -3(x - 140)(x - 4).
- P(0) = -1680
Step-by-step explanation:
Given
P(x) = -3x² + 432x - 1680
Required
- Find equivalent of P(x)
- Find P(x) when x = 0
To find the equivalent of P(x), we simply factorize P(x) = -3x² + 432x - 1680.
This is done as follows
P(x) = -3x² + 432x - 1680
P(x) = -3x² + 12x + 420x - 1680
P(x) = -3x(x - 4) + 420(x - 4)
P(x) = (-3x + 420)(x - 4)
Further expand -3x + 420
P(x) = -3(x - 140)(x - 4).
Hence, the equivalent of
P(x) = -3x² + 432x - 1680
without changing its form is
P(x) = -3(x - 140)(x - 4).
When price is 0, then x = 0.
Substitute 0 for P(x) in P(x) = -3(x - 140)(x - 4).
P(0) = -3(0 - 140)(0 - 4).
P(0) = -3(-140)(-4)
P(0) = -1680
Hence, the profit when price is 0 is -1680
