Question

Find the equation of the parabola that passes through the points (2, 127), (3,141), and (5,73). Use a system of equations and matrices for full credit. Leave your answer in the form y = ax² + bx + c.

Option 1: y = -5x² + 32x + 117
Option 2: y = 4x² - 11x + 118
Option 3: y = -2x² + 15x + 120
Option 4: y = 3x² - 7x + 127

Answer 1

The correct equation of the parabola that passes through the given points is derived from a system of equations resulting in y = -2x² + 15x + 120, which corresponds to Option 3.

Step-by-step explanation:

To find the equation of a parabola that passes through the points (2, 127), (3,141), and (5,73), we can set up a system of equations in the form y = ax² + bx + c for each point, resulting in three equations:

• 127 = 4a + 2b + c
• 141 = 9a + 3b + c
• 73 = 25a + 5b + c

These equations can be rewritten into matrix form as:

| 4 2 1 | | a | | 127 |
| 9 3 1 | | b | = | 141 |
| 25 5 1 | | c | | 73 |

By solving this system of equations, we can find the values of a, b, and c.

After solving the system, we find that a = -2, b = 15, and c = 120. Therefore, the correct parabolic equation is y = -2x² + 15x + 120, which corresponds to Option 3.