Question

Write the equation of a quadratic function that contains the points (1,21), (2,18), and (-1,9)

Answer 1

Answer:

The equation of a quadratic function that contains the points (1, 21), (2,18) and (-1, 9) is $y = -3\cdot x^{2}+6\cdot x +18$.

Step-by-step explanation:

A quadratic function is a second order 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.

From Algebra we understand that a second order polynomial is determined by knowing three distinct points. If we know that $(x_{1}, y_{1}) = (1, 21)$, $(x_{2},y_{2}) = (2,18)$ and $(x_{3}, y_{3}) = (-1, 9)$, then we construct the following system of linear equations:

$a+b+c = 21$ (2)

$4\cdot a + 2\cdot b + c = 18$ (3)

$a - b + c = 9$ (4)

By algebraic means, the solution of the system is:

$a = -3$, $b = 6$, $c = 18$

Therefore, the equation of a quadratic function that contains the points (1, 21), (2,18) and (-1, 9) is $y = -3\cdot x^{2}+6\cdot x +18$.