5. (MGSE9-12.A.CED.2, MGSE9-12.F.BF.1) Which equation is equivalent to $f (x) =$ $- 3 (x - 2)^{2} + 14 ?$
A. $f (x) = - 3 x^{2} + 2$
B. $f (x) = - 3 x^{2} + 26$
C. $f (x) = - 3 x^{2} - 4 x + 18$
D. $f (x) = - 3 x^{2} + 12 x + 2$

Answer

Expert–verified

Hide Steps

Answer

$f (x) = - 3 x^{2} + 12 x + 2$

Steps

Step 1 ：Expand the quadratic expression: $f (x) = - 3 (x - 2)^{2} + 14$

Step 2 ： $f (x) = - 3 (x^{2} - 4 x + 4) + 14$

Step 3 ： $f (x) = - 3 x^{2} + 12 x + 2$