# If f(x) = ax2 + bx + c and f(0) = 2, f(1) = 1 and f(4) = 6, then let us calculate the values of a, b and c.

We have,

f(x) = ax2 + bx + c …(i)

f(0) = 2

f(1) = 1

f(4) = 6

Replace x by 0 in equation (i), we get

f(0) = a(0)2 + b(0) + c

2 = 0 + 0 + c [ f(0) = 2]

2 = c

c = 2 …(ii)

Now, replace x by 1 in equation (i), we get

f(1) = a(1)2 + b(1) + c

1 = a + b + 2 [ f(1) = 1 & c = 2]

a + b = 1 – 2

a + b = -1 …(iii)

Finally, replace x by 4 in equation (i), we get

f(4) = a(4)2 + b(4) + c

6 = 16a + 4b + 2 [ f(4) = 6 & c = 2]

16a + 4b = 6 – 2

16a + 4b = 4

4 (4a + b) = 4

4a + b = 1 …(iv)

Solving equations (iii) & (iv), we get

-3a = -2

Put a = 2/3 in equation (iii), we get

Thus, a = 2/3, b = -5/3 and c = 2.

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