Final answer:
The equation of a parabola that opens downward through the points (-6, 0), (0, 6), and (20, 16) is found by solving a system of equations derived from the standard quadratic form y = ax² + bx + c using the given points to find the specific constants a, b, and c.
Step-by-step explanation:
The equation of a parabola that opens downward and passes through the given points can be expressed in the standard quadratic form y = ax² + bx + c, where a, b, and c are constants. Since the parabola opens downward, the coefficient a will be negative. To find the specific equation, we will use the three given points (-6, 0), (0, 6), and (20, 16) to create a system of equations:
- 0 = a(-6)² + b(-6) + c
- 6 = a(0)² + b(0) + c
- 16 = a(20)² + b(20) + c
By solving this system of equations, we determine the values of a, b, and c that satisfy all three points. After solving, we will obtain the specialised quadratic equation y = ax² + bx + c that represents the parabola in question.