Identify the domain and range for the graph of y = −2x2 − 8x + 1

Question

myininaya · Answer

domain for all polynomials is all real numbers! :)
now the best thing to do is put this into this form
$$y=a(x-h)^2+k $$
to find the range
This form is called vertex form by the way!

myininaya · Answer

or i guess you could look at visually but i don't care for that

myininaya · Answer

$$y=-2(x^2+4x)+1$$
$$y=-2(x^2+4x+(\frac{4}{2})^2)+1+2(\frac{4}{2})^2$$
Notice I added in a[b/2]^2 So I had to take it out! :)
Now we have
$$y=-2(x+2)^2+1+2(\frac{16}{4})=-2(x+2)^2+1+8$$
$$y=-2(x+2)^2+9$$
I see that the vertex is (-2,9)
|dw:1331078112680:dw|
That means the range is $$[-\infty,9]$$

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