Identify the axis of symmetry and vertex of f(x) = –2x^2 –2x–1.
Axis of symmetry: x = 0.5; Vertex: (0.5, – 0.50)
Axis of symmetry: x = – 0.5; Vertex: (– 0.5, 0.50)
Axis of symmetry: x = – 0.5; Vertex: (– 0.5, – 0.50)
Axis of symmetry: x = 0.5; Vertex: (– 0.5, – 0.50)

- anonymous

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- anonymous

@fashionismybesty

- anonymous

http://www.mathway.com/graph/NTUxODk
this is an amazing site for graphing

- freckles

Do you know how to write in vertex form? If involves completing the square?
\[f(x)=-2x^2-2x-1 \\ f(x)=-2(x^2+x)-1 \\ f(x)=-2(x^2+x+L)-1+2L \\ \text{ notice } -2L+2L=0 \\ \text{ we need to figure out what } L \text{ needs to be to } \\ \text{ complete the square inside that one ( )}\]

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## More answers

- triciaal

|dw:1440639916432:dw|

- triciaal

vertex form a(x-h)^2 + k = 0
vertex (h, k)
axis of symmetry x = h

- anonymous

It's really confusing.

- Nnesha

do you know what 's a b and c in the equation ?

- anonymous

No.. I'm really confused with math, I sometimes know things but like need to refresh my mind.. I know some rules in Arabic and some in English.. Because I took math in both languages and now im really really confused

- Nnesha

\(\color{blue}{\text{Originally Posted by}}\) @Nnesha
or
http://openstudy.com/study#/updates/55de281ae4b0f9297e9bc5e7
:=)
\(\color{blue}{\text{End of Quote}}\)
didn't notice that link doesn't work
http://openstudy.com/study#/updates/55daa403e4b0a0d51271c948

- Nnesha

ahh i see okay

- Nnesha

quadratic equation is \[\huge\rm Ax^2+Bx+C=0\]
where
a=leading coefficient
b=middle term
c= constant term

- Nnesha

quadratic equation is \[\huge\rm\color{red}{ A}x^2+\color{blue}{B}x+\color{pink}{C} \]
where
a=leading coefficient
b=middle term
c= constant term
\[\huge\rm \color{Red}{–2}x^2 \color{blue}{–2}x\color{pink}{–1}\]
so what is a and b equal to in that equation ?

- Nnesha

let me if u didn't understand :=)

- anonymous

2? @Nnesha

- Nnesha

not just negative 2
a=-2
b=-2 now use the formula to find x-coordinate of vertex \[\huge\rm \frac{ -b }{ 2a }\]
replace b and a with -2

- anonymous

so it would be -2/2^-2?

- Nnesha

no \[\frac{ -(-2) }{ 2(-2)}\]
don't forget to put the parentheses there is negative sign in the formula and b is also negative
and at the denominator it's 2 times -2 not 2 to the -2 power

- Nnesha

2(-2) is n't same as 2^(-2)

- anonymous

Ohh okay

- Nnesha

now simplify that

- anonymous

it would equal -2?

- Nnesha

no

- Nnesha

\[\huge\rm \frac{ -(-2) }{ 2(-2)}\]
what did you get at the numerator ?

- anonymous

aren't we supposed to divide the numerator and denominator by -2

- Nnesha

yes right \[\huge\rm \frac{ -\cancel{(-2)} }{ 2\cancel{(-2)}}\]
what would you get at the top ?

- anonymous

the negative sign

- anonymous

0?

- Nnesha

no there is one

- Nnesha

invisible one :=)

- Nnesha

so it should be -1/2

- Nnesha

just like 2/2 =1

- anonymous

Oh okay

- Nnesha

yes so that's the x-coordinate of the vertex which is also the axis of symmetry

- Nnesha

now replace all x for -1/2 into the f(x) function

- Nnesha

\[\huge\rm f(-0.5) = –2x^2 –2x–1.\] -1/2 = -0.5
so now replace all x's for -0.5 then solve

- anonymous

f(-0.5) = -2(-0.5)^2-2(0.5)-1

- Nnesha

yes right now solve right side :=) to find y-coordinate of the vertex

- anonymous

equals -0.5?

- Nnesha

yes right that's y-coordinate of vertex

- Nnesha

done!

- anonymous

but the choices have 0.50.. from where did that come from @Nnesha

- Nnesha

ohh that's the same .50 or .5

- anonymous

so the answer is C) Axis of symmetry: x = – 0.5; Vertex: (– 0.5, – 0.50)

- Nnesha

yep

- Nnesha

subtract .50-.5 you will get 0 thats mean both are the same

- anonymous

Oh thank you very much!

- Nnesha

my pleasure!

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