Question

Where is the vertex of the graph of f(x)= |x+2|+4? I will give medals

Answer 1

`f(x−h)`
here h is horizontal shift
`f(x) + k` here k is vertical shift
y=a(x-h)^2+k
whihc is same as y=aIx-hI+k
if h is negative graph will shift h unit to the right
if h is positive graph will shift h unit to the left
if k is positive graph shift k unit upp
if k is negative some unit down

Answer 2

Uh what?

Answer 3

oh vertex.
vertex form equation where \[\rm y=a \left| x-h \right|+k\] (h,k) is the vertex

Answer 4

So what's the vertex for my problem?

Answer 5

Your equation:
\[f(x)= |x+2|+4\]
general vertex form equation:
\[f(x) = a|x-h|+k\]compare the two and figure out the values of \(a,h,k\) you need to make them identical. Your vertex will be at \((h,k)\)

Answer 6

So my answer is (2,4)?

Answer 7

there is a negative sign in the original equation
\[\rm y=a \left| x \color{ReD}{-h} \right|+k\]
now compare ur equation \[\rm y=a \left| x \color{ReD}{+2} \right|+4\]
which is same as as \[\rm y=a \left| x -\color{ReD}{(-2)} \right|+4\]
- times - = positive 2
or in other words if there is `+h` then x-coordinate of the vertex would be negative
and if it's `-h` then x-coordinate would be positive

Answer 8

There is a great deal of educational value in checking your work! Got an answer for this problem? Make a graph from the equation and see if you get the vertex in the same place.

It may seem like mindless tedium, but actually going through the motions of doing the work, rather than simply reading someone else's work and saying "uh huh" will result in much better understanding and proficiency.