Answer:
The equation of a quadratic function that contains the points (1, 21), (2,18) and (-1, 9) is [tex]y = -3\cdot x^{2}+6\cdot x +18[/tex].
Step-by-step explanation:
A quadratic function is a second order 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[/tex], [tex]b[/tex], [tex]c[/tex] - Coefficients.
From Algebra we understand that a second order polynomial is determined by knowing three distinct points. If we know that [tex](x_{1}, y_{1}) = (1, 21)[/tex], [tex](x_{2},y_{2}) = (2,18)[/tex] and [tex](x_{3}, y_{3}) = (-1, 9)[/tex], then we construct the following system of linear equations:
[tex]a+b+c = 21[/tex] (2)
[tex]4\cdot a + 2\cdot b + c = 18[/tex] (3)
[tex]a - b + c = 9[/tex] (4)
By algebraic means, the solution of the system is:
[tex]a = -3[/tex], [tex]b = 6[/tex], [tex]c = 18[/tex]
Therefore, the equation of a quadratic function that contains the points (1, 21), (2,18) and (-1, 9) is [tex]y = -3\cdot x^{2}+6\cdot x +18[/tex].
