Part 1:

Find the vertex, axis of symmetry, domain, and range of the graph of y = −2x^2 − 6x + 1.


Part 2:

Using complete sentences, explain how you can determine the axis of symmetry, the domain, and range without graphing y = −2x^2 − 6x + 1.

Verified Answer :

The following are the answers to
the questions presented:

Part 1:

Vertex: (−3/ 2, 11/2)

Axis of
symmetry = x = -3/2

Domain = all
real numbers

Range = y ≤ 11/2

Part 2:

A quadratic equation is symmetrical around its vertex. The
equation for the axis of symmetry is x = -3/2 since the equation is in terms of
x. Since no value of x is undefined, then the domain of the equation is clearly
all real numbers. Since the value of “a” is negative, then that means the y
coordinate of the vertex is the maximum value so the range will never get above
11/2. I am hoping that these answers have satisfied your queries and it
will be able to help you in your endeavors, and if you would like, feel free to
ask another question.