Question

The function A = 12x - x2, where x is width in meters, gives the area A of a pond in square meters. Graph the function and use the graph to determine the width that gives the greatest area.
a. 6 m
b. 8 m
c. 7.5 m
d. 10.5 m

Answer 1

A = 12x - x2
is the x2 mean x squared?

Answer 2

yes, sorry. its x^2

Answer 3

ok!
lets rearrange the equation so it's more friendly to graph

Answer 4

A = 12x - x2
let y = A then we have
Y = -x^2 + 12x

so we are to graph this, so lets pick a few numbers for x, say, 0, 2, 5, and 7? lets plug those in, get y, then draw up a graph,
can you plug in 0, 2, 5, and 7 and get the value for y for each?

Answer 5

ok, i will, one second :)

Answer 6

ok, i got
0,0
2,20
5,35
7,35
are those right?

Answer 7

yes they are good, thats what I got

(x, y)
(0, 0)
(2, 20)
(5, 35)
(7, 35)

so now we have the points, we can draw up a graph that would look something like the real one, which we can use to find the answers for parts a, b, c, and d

Answer 8

now on your homework, draw up a coordinate system like this one, and make you x and y axis both 0 to 35

Answer 9

ok, im doing that now

Answer 10

or you can draw it like this..

Answer 11

ok, ill do the second one

Answer 12

good choice!

Answer 13

ok, i drew it on my paper

Answer 14

so your graph should look something like this...