Question

Write the quadratic function f(x) = 3x2 - 6x + 9 in vertex form. A) f(x) = 3(x - 3)2 + 9 B) f(x) = 3(x - 1)2 + 6 C) f(x) = 3(x + 3)2 + 6 D) f(x) = 3(x + 1)2 + 9

Answer 1

Answer:

Option B $f(x)=3(x-1)^{2}+6$

Step-by-step explanation:

we have

$f(x)=3x^{2} -6x+9$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)-9=3x^{2} -6x$

Factor the leading coefficient

$f(x)-9=3(x^{2} -2x)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$f(x)-9+3=3(x^{2} -2x+1)$

$f(x)-6=3(x^{2} -2x+1)$

Rewrite as perfect squares

$f(x)-6=3(x-1)^{2}$

$f(x)=3(x-1)^{2}+6$ ------> equation in vertex form

the vertex is the point $(1,6)$