The population of mosquitoes in a certain area as a function of inches of rainfall is modeled in the table. the function is quadratic, rainfall(in.) .population (millions.) 0. 0 1. 9 3. 21 4. 24 5. 25 6. 24 the x-intercept represents that after in. of rain there are mosquities. ( i cant seem to wrap my head around this, if you can just me start somehwere i'd really appriciate it. also i noticed the pattern in mosquitoes.)

The x-intercept represents that after 10  in. of rain there are mosquitoes.

                        Or

The x-intercept represents that after 0 in. of rain there are no mosquitoes.

Step-by-step explanation:

We are given a table that represents the population of mosquitoes in a certain area as a function of inches of rainfall :

RAINFALL(in.)     POPULATION (millions.)

     0                               0

      1                                9

      3                              21

      4                              24

      5                              25

      6                              24

We will first find the function P(t) which denotes the number of mosquitoes after t inches of rainfall.

As the function is quadratic.

Hence , let:

At t=0 we have, P(t)=0

at t=1 we have: P(t)=9

i.e.

Also at t=2 we have: P(t)=21

i.e.

On solving equation (1) and (2) we get:

a= -1 and b=10

Hence,

We know that the x-intercept of a graph is a point where the y-value is zero.

i.e. it is the inches of rainfall when the population of mosquitoes is zero i.e. there are no mosquitoes.

i.e. we have to find t such that:

P(t)=0

i.e.

Hence, we have got two x-intercept.

one at t=0 and the other at t=10.

The x-intercept represents that after 10 in. of rain there are no mosquitoes.

         Or

The x-intercept represents that after 0 in. of rain there are no mosquitoes.

The x-intercept represents that after 10 in. of rain there are mosquitoes.

Step-by-step explanation:

The population of mosquitoes in a certain area as a function of inches of rainfall is modeled in the table.

The function is quadratic,

where, P represents number of mosquitoes in millions. x represents rainfall in inches.

Table :

   x  :   0       1       3       4       5       6  

  P   :  0       9      21      24     25    24

Using three point to make system of equation and solve for coefficients a, b and c

Put (0,0) and we get  

Put (1,9) and we get

Put (3,21) and we get

Solve for a, b and c

Now, we will find x-intercept of the function. Put P(x)=0 and solve for x

The x-intercepts represent number of mosquitoes after 10 in of rain fall.