Question

What is the equation in standard form of the parabola containing the following points: (0, 1), (1, 5), and (2, 3)?

A) y = 2x^2 - 3x + 1
B) y = x^2 - 2x + 1
C) y = -2x^2 + 3x + 1
D) y = -x^2 + 2x + 1

Answer 1

After substituting the given points into the quadratic equation y = ax² + bx + c and solving the system of equations, we find that the standard form of the equation for the parabola is y = 3x² - 2x + 1, which is not listed among the provided options.

Step-by-step explanation:

The question involves determining the equation of a parabola in standard form that passes through three given points: (0, 1), (1, 5), and (2, 3). To find the appropriate equation, we need to solve for the coefficients 'a', 'b', and 'c' in the quadratic equation y = ax² + bx + c. We can substitute the points into the equation to create a system of equations:

• 1 = a(0)² + b(0) + c
• 5 = a(1)² + b(1) + c
• 3 = a(2)² + b(2) + c

By solving this system, we find that:

• c = 1
• 5 = a + b + 1
• 3 = 4a + 2b + 1

Subtracting the first equation from the other two gives:

• 4 = a + b
• 2 = 4a + 2b

Dividing the last equation by 2, we get 1 = 2a + b. Subtracting this from the second to last gives 3 = a, and substituting 'a' back into the equation, we find that b = -2. Hence, the correct equation is y = 3x² - 2x + 1, which is not listed in the multiple-choice options provided, implying a possible error in the question or the options.