Question

What is the turning point of the graph of f(x) = |x – 4| ?

Answer 1

|x – 4| <--- what value of "x" makes that expression = 0?

Answer 2

Ix-4I is x-4

Answer 3

i dont know.. o.O

Answer 4

Just to make sure you understand what |....| means...
What is |-4| ?
What is | 7 | ?

Answer 5

what's -4? what is 7? i dont get it?

Answer 6

Those 2 lines mean "absolute value"
To take the "absolute value" of a number means simply this:
If it is negative, change it to positive.
If it is not negative, leave it alone.
|-4| = 4
| 7 | = 7

Answer 7

What do you need to replace x with to make x - 4 be 0 ?

Answer 8

0?

Answer 9

let us try a few values for "x" see if they work to make it 0
\(\large \begin{array}{llll}
x\qquad &f(x)\\
\hline\\
{\color{blue}{ 5}}& |{\color{blue}{ 5}} - 4|\implies |1|\implies 1\\
{\color{blue}{ 2}}&|{\color{blue}{ 2}} - 4|\implies |-2|\implies 2\\
{\color{blue}{ -7}}&|{\color{blue}{ -7}} - 4|\implies |-11|\implies 11\\
\end{array}\)

so... those values didn't work
so... what do you think will work for "x" to make the expression 0?

Answer 10

0 x 4?

Answer 11

well, yes if we were multiplying times 4, but we're not
we're just subtracting

Answer 12

x - 4 = 0
x = 4
f(4) = |x - 4| ?

Answer 13

ohhh so if we set x = 4, then the expression turns 0, I see so \(\bf f(x) = |x - 4| \implies f(x) = |x - 4| +0
\\ \quad \\
|{\color{red}{ 4}} - 4| +{\color{red}{ 0}}\\
({\color{red}{ 4,0}})\Leftarrow \textit{"turning point" or }vertex\)

Answer 14

thank you all :]

Answer 15

yw