Question

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.

Answer 1

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.