Question

Part 1 − Find the vertex, axis of symmetry, domain, and range of the graph of y = −2x2 − 6x + 1. Show all work for full credit.

Part 2 − Using complete sentences, explain how you can determine the axis of symmetry, the domain, and range without graphing y = −2x2 − 6x + 1.

Answer 1

Part 2:
The axis of symmetry is found by taking the additive inverse (negative) of the middle coefficient and dividing it by two times the leading coefficient. Because the independent variable is x, the line of symmetry will take the form of x=number. Also because x is the independent variable, the domain is the set of all real numbers. The range can be determined by calculating the value of y, given the x determined above as the axis of symmetry. If the leading coefficient is positive, this y-value will be the lower most value in the range and it will take the form y>=number. If the leading coefficient is negative, this y-value will be the upper most value in the range and the range will take the form y<=number.

Part 1 can be found by applying part 2.