Question

y=-(x+2)(x-4)
find the domian,range,axis of symmetry

Answer 1

@welshfella

Answer 2

HI!!

Answer 3

first step would be to multiply this out

Answer 4

Okay

Answer 5

let mt know what you get

Answer 6

then we can finish quickly

Answer 7

Alright, hold on:)

Answer 8

-x^2+2x+8

Answer 9

ok good

Answer 10

:)

Answer 11

now the fact that the leading coefficient it negative ( it is \(-1\)) means this parabola opens down
all that is left is to find the vertex

Answer 12

the first coordinate of the vertex of \(y=ax^2+bx+c\) is
\[-\frac{b}{2a}\] which in your case is
\[-\frac{2}{2\times (-1)}\]

Answer 13

1

Answer 14

right
and the second coordinate is what you get for \(y\) when you replace \(x\) by \(1\)

Answer 15

9

Answer 16

right again

Answer 17

so lets answer each question in order

Answer 18

d=all real #'s right?

Answer 19

Find the domian
the domain of an polynomial is \(\mathbb{R}\) what you said

Answer 20

the range
since it is a parabola that opens down, and has a maximum at \(y=9\) the range is?

Answer 21

y>=-9

Answer 22

oh no

Answer 23

Oh:( Ok

Answer 24

not sure where you got the \(-9\) from it is \(9\) right?

Answer 25

yes, whoops!

Answer 26

and also the parabola opens down
that means the MAXIMUM value is 9, not the minimum value

Answer 27

is maximum <=,>= or <,>

Answer 28

lets forget about rules and think
the possible values for \(y\) are numbers less than or equal to 9

Answer 29

Alright

Answer 30

if you want to write it as an inequality you can write
\[y\leq 9\] or as an interval
\[(-\infty, 9]\]

Answer 31

okay, I see :)

Answer 32

and finally, the axis of symmetry which we found ages ago is \(x=1\)

Answer 33

done right?

Answer 34

yes:)

Answer 35

Thank you:)

Answer 36

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