Find the vertex and the axis of symmetry of the graph of the function: f(x) = -2x2 – 4x?

Question

Find the vertex and the axis of symmetry of the graph of the function:   f(x) = -2x2 – 4x?

anonymous · Answer

The first step would be to find the vertex. Do you know how to write a given parabola in vertex form?

anonymous · Answer

no

anonymous · Answer

One way is to complete the square. It allows you to rewrite the standard form $ax^2+bx+c$ into vertex form $(x-h)^2+k$, where $(h,k)$ is the vertex.

So we're given
$$y=-2x^2-4x$$
Do you know how to complete the square?

anonymous · Answer

is it -1 and-4?

anonymous · Answer

aaa or -6 -4

anonymous · Answer

$$\begin{align*}y&=-2x^2-4x\
&=-2\left(x^2+2x\right)\
&=-2\left(x^2+2x+1-1\right)\
&=-2\left((x+1)^2-1\right)\
&=-2(x+1)^2+2\
\end{align*}$$
What's the vertex?

anonymous · Answer

lost because is not the answer in the back of my book

anonymous · Answer

Well, according to my work, the vertex is $(-1,2)$, and Wolfram agrees: http://www.wolframalpha.com/input/?i=vertex+of+-2x%5E2-4x

anonymous · Answer

sorry looks like i didnt put this at the end of the question What are the x-intercepts of y = f(x-7

anonymous · Answer

of $y=f(x-7)$ or $f(x)-7$ ?

anonymous · Answer

the first one

anonymous · Answer

Okay. If $f(x)=-2x^2-4x$, then what is $f(x-7)$ ?

anonymous · Answer

no clue lol

anonymous · Answer

Plug in $x-7$:
$$\begin{align*}f(x)=-2x^4-4x~~\Rightarrow~~f(x-7)&=-2(x-7)^2-4(x-7)\
&=-2\left(x^2-14x+49\right)-4x+28\
&=-2x^2+28x-98-4x+28\
&=-2x^2+24x-70\end{align*}$$
Make sense so far?

anonymous · Answer

yes thanks

anonymous · Answer

the problem is thisFind the vertex and the axis of symmetry of the graph of the function:   f(x) = -2x^2 – 4x

anonymous · Answer

and this are the answers (-1,0); x = -1
       (-1,2); x = -1
       (1,2); x = 1
       (1,0); x = 1

anonymous · Answer

which am still not sure off

anonymous · Answer

Hmm, something's not working with the equation editor. Give me a moment to write it out.

anonymous · Answer

k thanks

anonymous · Answer

|dw:1378269651664:dw|
So what's the vertex?

anonymous · Answer

1-1

anonymous · Answer

Hmm? You should be getting a vertex of $(6,2)$... http://www.wolframalpha.com/input/?i=vertex+of+-2%28x-7%29%5E2-4%28x-7%29

anonymous · Answer

mmm

anonymous · Answer

i think the book is confusing me

anonymous · Answer

Answer key could be mismatched with a different question.

anonymous · Answer

yea

anonymous · Answer

thanks though

anonymous · Answer

yw