CAT 2007 — QA Question 2
Graph & Maximum or Minimum value of Quadratic functionEasy
A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value of f(x) at x = 10?
Answer & solution
- A
–119
–159
- C
–110
- D
–180
- E
–105
Solution
Let f(x) = px2 + qx + k, where p, q and k are integers, and p ≠ 0
Given, f(0) = k = 1
∴ f(x) = px2 + qx + 1
f(x) will attain maximum value at x = -q/2p
Now f(x) attains maixmum at x = 1
∴ x = 1 = -q/2p
⇒ q = -2p
Maximum value of f(x) = 3 = p(1)2 + q(1) + 1
⇒ 3 = p + q + 1
⇒ 3 = p - 2p + 1
⇒ p = -2 and q = 4
∴ f(x) = −2x2 + 4x + 1
⇒ f(10) = −200 + 40 + 1 = −159
Hence, option (b).