Question

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

Answer 1

Answer:  First Option

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

Step-by-step 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 $(-\frac{b}{2a}, f(\frac{-b}{2a}))$

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:

$(-\frac{(-2)}{2(1)}, f(\frac{2}{2(1)}))$

$(1, f(1))$

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 :

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