Question

Use the zeros and the labeled point to write the quadratic function represented by the graph.​

Answer 1

The quadratic function represented by the graph is
`y = x^(2)-6\cdot x + 8`.

Explanation:

Parabolae are defined by second order polynomials, that is, a polynomial of the form:

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

Where:

`x` - Independent variable.

`y` - Dependent variable.

`a, b, c` - Coefficients.

By Algebra, we know can calculate the set of all coefficients based on the knowledge of three distinct points. According to the graph, we have the following points:
`(x_(1), y_(1)) = (2, 0)`,
`(x_(2), y_(2)) = (4, 0)` and
`(x_(3), y_(3)) = (6, 8)`, and the resulting system of linear equations is:

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

`16\cdot a + 4\cdot b + c = 0` (3)

`36\cdot a + 6\cdot b + c = 8` (4)

The solution of the system of linear equations is:

`a = 1, b = -6, c = 8`

Hence, the quadratic function represented by the graph is
`y = x^(2)-6\cdot x + 8`.