Using the table below find a formula for the polynomial func

Using the table below find a formula for the polynomial function of degree 2. h(x) =

Solution

x   1   2    3   4

h(x)4   5   10 19

We have to find a function of degree 2

It means we have to find a quadratic equation and quadratic equation is of the form

f(x)=ax²+bx +c

at x=1,h(x)=4

4= a+ b+c

at x=2 ,h(x)=5

5= 4a + 2b+c

at x=3,h(x)=10

10=9a + 3b+c

So we have three equations

a+b+c=4

4a + 2b+c=5

9a +3b+c=10

From first and second equations,we get

3a+b=1

And from first and third we get

8a + 2b=6

4a+b=3

Now we have

3a+ b=1

4a+b=3

From these two equations,we get a=2

3a+b=1

3(2)+b=1

b=-5

a+b+c=4

2-5+c=4

c=7

Hence the required polynomial is

f(x)= 2x²-5x+7