Question

The image shows a geometric representation of the function f(x) = x2 – 2x – 6 written in standard form.



What is this function written in vertex form?


f(x) = (x –1)2 – 7

f(x) = (x +1)2 – 7

f(x) = (x –1)2 – 5

f(x) = (x +1)2 – 5

Answer 1

A is the correct answer i believe

Answer 2

Answer : A)  $f(x) = (x-1)^2 - 7$

Standard form of equation is $f(x) = x^2 - 2x - 6$

The vertex form of equation is $y= (x-h)^2 + k$

where (h,k) is the vertex

To find x coordinate of vertex we use formula $h =\frac{-b}{2a}$

$f(x) = x^2 - 2x - 6$, a=1, b=-2 and c=-6

Plug in the values

$h =\frac{-b}{2a}=\frac{-(-2)}{2*1}= 1$

Now plug in x=1 in the equation

$k =f(x) = 1^2 - 2(1) - 6 = 1-2-6= -7$

h= 1  and k=-7

The vertex form of equation is $y= (x-h)^2 + k$

Plug in the values h=1 and k=-7

$f(x)= (x-1)^2 - 7$