Question

Use the Function to answer the question:

f(x)=-2|x-5|+3

What is the vertex of the graph of f(x)?

a. (-5,3)
b. (-2,3)
c.(5,-3)
d. (5,3)

Answer 1

notice the absolute value expression

what value of "x" makes that absolute expression = 0?

Answer 2

Hmmm well -5 is in the absolute value. would that be it?

Answer 3

x = -5?

Answer 4

well... let's say we give "x" some value
what value given to "x" would make the absolute value expression = 0, I meant

Answer 5

I'm horrible at math. but to my understanding... in order to find the value of "x" I need to see what I would plug in for it to see if that equals 0?

Answer 6

In that case... I can honestly say I am not sure. I am sorry.

Answer 7

let us look at the absolute value expression \(\large | x- 5|\)
let us use say x = 7 so if we set x = 7 then | (7) -5 | => | 2 | => 2

so... setting x = 7 doesn't make the expression 0, it actually makes is 2

any ideas on what we could use for "x" to make the expression 0?

Answer 8

keep loosing connection. Let me read what you said

Answer 9

OH! Sorry. I understand what you're saying now. we could put 5 as the value of "x" to get 0 because 5-5=0

Answer 10

yeap thus \(\large {
f(x)=-2|x-5|+3
\begin{cases}
-2|{\color{brown}{ 5}}-5|{\color{blue}{ +3}}
\\ \quad \\
({\color{brown}{ 5}},{\color{blue}{ +3}})\impliedby vertex
\end{cases}
}\)

Answer 11

Oh, awesome!! Thanks so much jdoe001!!

Answer 12

yw