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

c.

8 m


b.

7.5 m

d.

10.5 m

Answer 1

@charlotte123

Answer 2

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 3

can you plug in 0, 2, 5, and 7 and get the value for y for each?

Answer 4

my graph wont let me

Answer 5

(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 6

Do you prefer a graph like this:





Or do you prefer a graph like this:

Answer 7

the first

Answer 8

A = 12(6) - 6^6 <--- A = -46584
A = 12(8) - 8^8 <---- A = -16777120
And so on -
The larger the numbers get - The more the Area decreases

Answer 9

If you do the second choice, your graph should look something like this:

Answer 10

so, the x^2 in the equation tells us that it is a parabola, so lets plug in one more random number into the equation, so we can get the curve to come back down to the x-axis, so do x=11 and get y, and put that point on your graph


So if you use that graph I just wrote above, then it should now look like this: