Question

It is given that f(x) = 2x2 - 12x + 10.

(i) Find the value of a, of b and of c for which f(x) = a(x + b)2 +c.​

Answer 1

a = 2, b = - 3, c = - 8

Explanation:

Expand f(x) = a(x + b)² + c and compare coefficients of like terms, that is

a(x + b)² + c ← expand (x + b)² using FOIL

= a(x² + 2bx + b²) + c ← distribute parenthesis by a

= ax² + 2abx + ab² + c

Compare like terms with f(x) = 2x² - 12x + 10

Compare coefficients x² term

a = 2

Compare coefficients of x- term

2ab = - 12, substitute a = 2

2(2)b = - 12

4b = - 12 ( divide both sides by 4 )

b = - 3

Compare constant term

ab² + c = 10 , substitute a = 2, b = - 3

2(- 3)² + c = 10

18 + c = 10 ( subtract 18 from both sides )

c = - 8

Then a = 2, b = - 3, c = - 8