Final answer:
To determine the equation of the parabola, we plug the given points into the standard quadratic equation form and solve for coefficients a, b, and c. The resulting equation is y = -5x² + 3, which is not listed in the multiple-choice options provided.
Step-by-step explanation:
To find the equation of the parabola, we will use the given points to set up a system of equations. Recall that the standard form of a quadratic equation is y = ax² + bx + c. We can plug each point into this equation to create three equations for our three unknowns (a, b, c).
For the point (0, 3), we get the equation 3 = a(0)² + b(0) + c, which simplifies to c = 3. For the point (1, -2), we substitute to get -2 = a(1)² + b(1) + 3. Finally, for the point (3, 0), we substitute to get 0 = a(3)² + b(3) + 3.
Solving the system, we have:
- -2 = a + b + 3
- 0 = 9a + 3b + 3
From the first equation, subtracting 3 from both sides gives us -5 = a + b. Using this and the second equation, we can solve for a and b using elimination or substitution method.
When we solve this system, we get a = -5, b = 0, and c = 3. The main answer to the student's question is therefore, y = -5x² + 0x + 3, which simplifies to y = -5x² + 3. This equation is not listed in the options, which suggests there might be an error in the question or the options provided.