Question

Parabola passes through the points (0,5), (1,4), and (2,5). What function does the graph represent?

Answer 1

Answer:

x^2 - 2x + 5 = 0.

Step-by-step explanation:

The (0, 5) is the point where the parabola passes through the y axis (where x = 0), so we can write the equation as

y = ax^2 + bx + 5   where a and b are constants to be found.

Also, since (1, 4) and (2, 5) are points on the curve, substituting, we have the system:

a(1)^2 + 1b + 5 = 4

a(2)^2 + 2b + 5 = 5

Simplify these 2 equations:

a  + b  =  -1  .................(1)

4a + 2b = 0..................(2)

Multiply the first equation by -2:

-2a - 2b = 2 .................(3)

Add (2) + (3):

2a = 2

a = 1.

Substitute a = 1 into (2):-

4*1 + 2b = 0

2b = -4

b = -2.