Question

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

Answer 1

Answer:

The quadratic function represented by the graph is $y = x^{2}-6\cdot x + 8$.

Step-by-step 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 $y = x^{2}-6\cdot x + 8$.