Question

he following function shows the relationship between the selling price (s), and profit P(s), in dollars, for a company.

P(s) = -20s2 + 1,400s - 12,000

Which statement best describes the intervals where the company's profit increases, decreases, or records a maximum?

It is least when the selling price is $35.
It is greatest when the selling price is $35.
It decreases when the selling price increases from $10 to $35.
It increases when the selling price increases from $35 to $100. @preetha @dan815 @aaronq

Answer 1

@whpalmer4 @iGreen

Answer 2

@phi

Answer 3

is this calculus ?

Answer 4

Algebra 1

Answer 5

thats why i dont understand

Answer 6

do you recognize what kind of "curve" is created by your equation ?

Answer 7

well its a minimum

Answer 8

by curve, I mean , for example, straight line, parabola, hyperbola, ellipse, etc...

Answer 9

parabola

Answer 10

i think the answer is D?

Answer 11

no, wait, with the -20 s^2 it is \( \cap \) shaped

Answer 12

it is?

Answer 13

i graphed it on desmos i got a parabola

Answer 14

.You could do this problem in one or more of several ways.
If you're in Calculus, take the derivative of P with respect to s and set it = to 0.
If you're not in Calculus, but in Algebra, draw the graph of this polynomial.

Answer 15

but I would still find its vertex.
if you have
a x^2 + bx + c (or in your case, s instead of x)
the x value (s value) of the vertex is at x= -b/(2a)

Answer 16

how do i find that?

Answer 17

you match up your equation
\[ -20s^2 + 1,400s - 12,000 \\ a s^2 + b s + c \]
what is a and b (i.e. numbers in front of s^2 and s , respectively) ?

Answer 18

-20 and 1400

Answer 19

now do b/(2*a) using your numbers
what do you get ?

Answer 20

-35?

Answer 21

oops, sorry, use -b/(2a)

Answer 22

35

Answer 23

it increase when the selling price increases from $10 to $35

Answer 24

so here is what you know: when s (selling price) is 35, you are at the peak of the parabola

Answer 25

okay

Answer 26

so B?

Answer 27

very roughly it looks like this