Question

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

Answer 1

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!

Answer 2

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

Answer 3

\[y=-2(x^2+4x)+1\]
\[y=-2(x^2+4x+(\frac{4}{2})^2)+1+2(\frac{4}{2})^2\]
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)

That means the range is \[[-\infty,9]\]

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