Theory question 102
PolynomialsExpress 3x2 − 6x + 10 in the form a(x − b)2 + c where a, b and c are integers. Hence state the minimum value of 3x2 − 6x + 10 and the value of x for which it occurs.
Show the model answer
Model answer
3x2 − 6x + 10 = 3(x2 − 2x) + 10 = 3(x − 1)2 − 3 + 10
= 3(x − 1)2 + 7, so a = 3, b = 1, c = 7
Since 3(x − 1)2 ≥ 0, the minimum value is 7, when x = 1
Explanation
Complete the square after taking out the factor 3.