Question

Write the equation, in standard form, of the parabola containing the following points:

(0, 1), (1, 5), (2, 3)
Student's Work
Student's Answer
A. y = -x2 + 5x + 3
B. y = 3x2 - 7x - 1
C. y = -3x2 + 7x + 1
D. y = -7x2 + 3x + 1

Answer 1

To find the equation of the parabola containing the points (0, 1), (1, 5), and (2, 3), we can substitute these points into the general form of the equation for a parabola, y = ax² + bx + c, and then solve the resulting system of equations.

Step-by-step explanation:

To find the equation of the parabola containing the points (0, 1), (1, 5), and (2, 3), we can substitute these points into the general form of the equation for a parabola, which is y = ax² + bx + c. Then we can solve the resulting system of equations to find the values of a, b, and c.

Using the point (0, 1):

1 = a*(0)² + b*(0) + c

c = 1

Using the point (1, 5):

5 = a*(1)² + b*(1) + 1

a + b = 4

Using the point (2, 3):

3 = a*(2)² + b*(2) + 1

4a + 2b = 2

Solving the system of equations:

a + b = 4

4a + 2b = 2

Multiplying the first equation by 2, we get:

2a + 2b = 8

Subtracting the second equation from the first, we get:

-2a = 6

a = -3

Substituting a = -3 into the first equation, we get:

-3 + b = 4

b = 7

Therefore, the equation of the parabola in standard form is:

y = -3x² + 7x + 1