Question

Use the points (0, 4), (1, 9), and (−3, 1) to write the equation for the quadratic function whose graph contains the

three points.

Answer 1

`P(x) = x^2 + 4x + 4`

Explanation:

For this case the quadratic function is given by this formula:

`P(x) = ax^2 + bx + c`

On this case we have the following points (0,4) ,(1,9) , (-3,1) so then we have the following 3 equations:

`4 = a(0)^2 +b(0) + c = c` (1)

From the equation (1) we have the value for c on this case c=4

`9 = a(1)^2 +b(1) + 4= a +b+4` (2)

`1 = a(-3)^2 +b(-3) + 4= 9a-3b +4` (3)

We can rewrite equations (2) and (3) like this:

`5= a+b` (2)

`-3 = 9a-3b` (3)

If we find a from equation (2) we got:

`a = 5-b` and we replace this into equation (3) we got:

`-3 = 9(5-b) -3b= 45-9b -3b = 45-12b`

`12b = 48, b = 4`

And then
`a = 5-4 = 1`

And then our equation for the polynomial would be:

`P(x) = x^2 + 4x + 4`