Let g (x) = x+2. Find f (x) if f (x) is a quadratic function of the form f (x) = ax^2+bx+c and f (g (x)) = 2x^2-x+3

Question

Mathematics

Yadira

11 October, 04:28

Let g (x) = x+2. Find f (x) if f (x) is a quadratic function of the form f (x) = ax^2+bx+c and f (g (x)) = 2x^2-x+3

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Lacey Harrison · Answer 1

Let g (x) = x + 2

f (g (x)) = 2x^2 - x + 3

= 2 (x^2 - x/2 + 3/2)

=2 (x^2 + 4x + 4) - 9x - 5

=2 (x+2) ^2 - 9 (x+5/9)

=2 (x + 2) ^2 - 9 (x + 2) + 13

f (x) = 2x^2 - 9x + 13