Answer:
The quadratic function represented by the graph is [tex]y = x^{2}-6\cdot x + 8[/tex].
Step-by-step explanation:
Parabolae are defined by second order polynomials, that is, a polynomial of the form:
[tex]y = a\cdot x^{2} + b\cdot x + c[/tex] (1)
Where:
[tex]x[/tex] - Independent variable.
[tex]y[/tex] - Dependent variable.
[tex]a, b, c[/tex] - 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: [tex](x_{1}, y_{1}) = (2, 0)[/tex], [tex](x_{2}, y_{2}) = (4, 0)[/tex] and [tex](x_{3}, y_{3}) = (6, 8)[/tex], and the resulting system of linear equations is:
[tex]4\cdot a + 2\cdot b + c = 0[/tex] (2)
[tex]16\cdot a + 4\cdot b + c = 0[/tex] (3)
[tex]36\cdot a + 6\cdot b + c = 8[/tex] (4)
The solution of the system of linear equations is:
[tex]a = 1, b = -6, c = 8[/tex]
Hence, the quadratic function represented by the graph is [tex]y = x^{2}-6\cdot x + 8[/tex].
