Question

Given the points (0, 5), (1, 7), and (-2, -5), find the equation of the quadratic polynomial that contains

these points. Show your work.

Answer 1

y=-x²+3x+5.

Explanation:

1) the common view of the quadratic function is y=ax²+bx+c, where a, b and c - numbers;

2) according to the equation above, it needed to substitute the given coordinates and to make up the system of the equations:

point (0;5): c=5;

poit(1;7): a+b+5=7 ('c' is already known, 5);

point(-2;-5): 4a-2b+5=-5 (c=5);

3) to solve the system:

`\left \{ {{a+b+5=7} \atop {4a-2b+5=-5}} \right. \ = > \ \left \{ {{a=-1} \atop {b=3}} \right.`

4) finally, if a=-1, b=3 and c=5, then

y=-x²+3x+5.