Question

Find a polynomial function whose graph passes through (7,13), (9,- 11), and (0,3).

Answer 1

Explanation:

I am going to assume this is a quadratic so

`f(x) = {ax}^(2) + bx + c`

When 3 is c

`{ax}^(2) + bx + 3`

When x is 7,

`a( {7}^(2) ) + b(7) + 3 = 13`

`49a + 7b = 10`

When x is 9,

`a(9) {}^(2) + 9b + 3 = - 11`

`81a + 9b = - 14`

We have two system, let's eliminate the b variable by multiplying the second system by

`(7)/(9)`

`63a + 7b = - (98)/(9)`

Bring down the first system

`49a + 7b = 10`

Subtract the two system,

`14a = ( - 188)/(9)`

`a = - (94)/(63)`

Plugging in a, we will eventually get

`b = (748)/(63)`

So our quadratic is

`- (94)/(63) {x}^(2) + (748)/(63) x + 3`