Determine a polynomial function whose graph passes through the given points. 5: (0,-5); (1,-4) ; (-1,-9); (2,-3),

The interpolating polynomial is

.

Step-by-step explanation:

First, notice that we want to calculate the interpolating polynomial through the points (0,-5); (1,-4) ; (-1,-9); (2,-3). This means that we want to find a polynomial such that

, and .

We will have four equations, so our polynomial will be, at most, of degree 3. Let us write

The coordinates give us the following equations:

Notice that from the second equation we know that . Then, we obtained the linear system of equations

which is equivalent to

.

So, we have reduced our interpolation problem to solve a linear system of equations. Now, notice that if we add the first two equations of the system we obtain

that yields .

Then, our system becomes

which is equivalent to

.

Recall that now the first two equations are just the same, so we will use the first and third ones:

.

If we multiply the first one and add it to the second we get:

that yields .

Thus, substituting this value in the first equation:

which is equivalent to . Then, .

Summing up all our results we get that the interpolating polynomial is

.

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.