Question

Find the quadratic polynomial whose graph goes through the points (-1,8), (0,6), and (2, 26). f(0) = x^2+ x+

Answer 1

4x² + 2x + 6 = 0

Explanation:

The polynomial which has highest degree 2 is known as quadratic polynomial. It is of the form:

ax² + bx + c = 0

where, a ≠ 0 and a, b & c are any constant.

We have given three points (-1, 8), (0, 6), and (2, 26)

Putting these value of (x, y) in quadratic equation one by one.

We get, three equations:

8 = a - b + c

6 = c

26 = 4a + 2b + c

Solving these equations, We get,

a = 4, b = 2 and c = 6

Now putting these values of a, b, and c in standard quadratic equation.

We get,

4x² + 2x + 6 = 0

which is required equation.