Question

Use the function to answer the question.
f(x) = -2|x - 5| + 3
What is the vertex of the graph of f(x)?
(Points : 4)
(-5, 3)

(-2, 3)

(5, -3)

(5, 3)

Answer 1

there is a rule with l x - 5l i know i wont have a negative

Answer 2

try drawing the graph

Answer 3

the 'V' is the graph of y = |x - 5|

now can u continue?

Answer 4

im still lost here

Answer 5

the |x-5| is obtained by defecting y = x-5 in the x axis (all values of y are positive

Answer 6

is it supposed to be 5,0?

Answer 7

no you now have to transform y = |x - 5| to y = -2|x - 5| + 3

the negative value will reflect the whole graph in x axis
and the + 3 will raise the whole graph by 3 units in y direction

Answer 8

so the v will be faced down and moved up 3 on the y axis?

Answer 9

so it would be 5,3

Answer 10

i'm a bit rusty with these - hold on a sec

Answer 11

ok :)

Answer 12

look at the absolute value expression, what value of "x" makes |x - 5| = 0?

Answer 13

cant remember jdoe will solve it

Answer 14

5-5 = 0

Answer 15

then \(\bf -2|x - 5| + 3\\ \quad \\
-2|(\color{red}{5}) - 5| \color{red}{+ 3}\\ \quad \\
(\color{red}{5\quad ,\quad 3})\Leftarrow vertex\)

Answer 16

ok i see thank you ^^

Answer 17

yw

Answer 18

of course - i had a mental aberation !!!