Question

Use the graph of the polynomial

function to find the factored form of
its related polynomial. Assume it
has no constant factor

Answer 1

The factored form of the polynomial is
`y = (x-2)\cdot (x+1)`.

Explanation:

According to the graph, we have a second order polynomial with a vertical axis of symmetry. The standard form of the polynomial is:

`y = a\cdot x^(2)+b\cdot x + c` (1)

Where:

`x` - Independent variable.

`y` - Dependent variable.

`a`,
`b`,
`c` - Coefficients.

We can obtain the solution of the polynomial by knowing three distinct points. From graph we know that the curve pass through the following three points:
`(x_(1),y_(1)) = (-1, 0)`,
`(x_(2),y_(2)) = (0, -2)`,
`(x_(3),y_(3)) = (2,0)`. Three linear equations are constructed:

`a^(2)-b+c = 0` (2)

`c = -2` (3)

`4\cdot a + 2\cdot b + c = 0` (4)

The solution of this system is
`a = 1`,
`b = -1` and
`c = -2`. Then, the polynomial in standard form is
`y = x^(2)-x-2`. By factorization, we find that factored form is:

`y = (x-2)\cdot (x+1)` (5)