Which function in vertex form is equivalent to f(x) = 4 + x2 – 2x? f(x) = (x – 1)2 + 3 f(x) = (x – 1)2 + 5 f(x) = (x + 1)2 + 3 f(x) = (x + 1)2 + 5

Question

asked Mar 22, 2020 118k views

1 Answer

Burax · Answer 1 · 2020-03-25T23:57:07+0000

Answer: First Option

f (x) = (x-1) ^ 2 + 3

Explanation:

Quadratic quadratic functions have the following form:

f (x) = (x-h) ^ 2 + k

Where the point (h, k) is the vertex of the function.

For a quadratic function of the form
f (x) = ax ^ 2 + bx + c the vertex of the function is at the point
(-(b)/(2a), f((-b)/(2a)))

In this case the function is:
$f(x) = 4 + x^2 - 2x\\\\f(x)=x^2 -2x +4$

Then:

$a=1\\b=-2\\c=4$

The vertex is:

(-((-2))/(2(1)), f((2)/(2(1))))

(1, f(1))

Note that

$f(1) = (1)^2 -2(1) +4\\\\f(1)=1-2+4=3$

Therefore the vertex is the point
(1, 3)

Finally we have that
$h=1,\ k=3$

The function in vertex form is :

f (x) = (x-1) ^ 2 + 3