Question

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

Answer 1

To express a function of the form $f(x)= x^{2} +bx+c$ in vertex form $f(x)=a(x-h)^2+k$ where (h,k) is the vertex of the parabola, we need to find the vertex first.
To find the vertex we are going to use the vertex formula: $h= \frac{-b}{2a}$, and $k$ will be the function evaluated at $h$.
We can infer from our function that $a=1$ and $b=-2$. So lets find $h$:
$h= \frac{-b}{2a}$
$h= \frac{-(-2)}{2(1)}$
$h= \frac{2}{2}$
$h=1$
Now that we have $h$, we can evaluate the function at 1 to find $k$:
$f(x)=4+ x^{2} -2x$
$f(1)=4+(1)^2-2(1)$
$f(1)=4+1-2$
$f(1)=3$

We have the vertex (1,3) of our parabola, so we can use its vertex form:
$f(x)=a(x-h)^2+k$
$f(x)=1(x-1)^2+3$
$f(x)=(x-1)^2+3$

We can conclude that the vertex for of our parabola is f(x) = (x + 1)2 + 3.

Answer 2

Answer:

A:

f(x) = (x – 1)2 + 3