Question

I can't figure this one out.. MEDAL AND FAN FOR ANYONE WHO CAN UN-CONFUZZLE ME!!

For the function f(x) = –(x + 1)2 + 4, identify the vertex, domain, and range.

Answer 1

Where are you stuck?

Answer 2

mostly the vertex

Answer 3

open parentheses, what do you have for f(x) ?

Answer 4

f(x)=-x+1^2+4

Answer 5

nnnnnnnnnnnnnope

Answer 6

\(f(x) = -(x+1)^2 +4\)
redo, please. Use Foil

Answer 7

-x+5? after you simplify ?

Answer 8

How do you find out the range aswell I vaguely remember

Answer 9

\((x+1)^2 =(x+1)(x+1)\) ,using Foil to open parentheses

Answer 10

Oh ya I forgot you had to do that with squared binomials

Answer 11

X^2+2x+1

Answer 12

Yup, don't forget, before them, you have - sign, after them you have +4
now, put all in, what do you get for f(x) ??

Answer 13

Where did you get the +4 from?

Answer 14

From the original problem.

Answer 15

Oh ok, did I mess up the foil? You said something about a negative and when I plugged 4 into \[x ^{2}+2x+1 \] I got 25 and that's not one of the choices for the y-coordinate and it doesn't really make sense

Answer 16

NOOOOOOOOOPe

Answer 17

\(f(x) = \huge \color{red}{-} (x+1)^2 +4\\~~~~~~~~~~=\huge\color{red}{-} (x^2+2x+1)+4\\=\huge -x^2-2x-1+4\)
ok??

Answer 18

hey!!! YES or NO?

Answer 19

OOHHH

Answer 20

YES got it :) but how bought the range? Ik the domains gunna be all real numbers

Answer 21

wait, simplify it, please.

Answer 22

don't know??? why?? -1+4 =?

Answer 23

3?

Answer 24

yes, so that \(f(x) =-x^2-2x+3\) right?

Answer 25

From this, the REAL process starts.

Answer 26

what are a, b, c on it?

Answer 27

a=?
b=?
c=?

Answer 28

a=-1 b=-2 c=3

Answer 29

yup, hence the vertex has x-coordinate is \(x= -b/2a\) , hence x =??

Answer 30

x=4

Answer 31

\(x=-\dfrac{b}{2a}=-\dfrac{-2}{2*(-1)}=??\)

Answer 32

1

Answer 33

so the vertex is 1,4?

Answer 34

TY FOR HELPING ME FIGURE HAT PART OUT :)))) but how do I know what the range is going to be?

Answer 35

to it, when you have vertex, and the parabola is downward, hence the range is from - infinitive to y-coordinate of the vertex.