Question

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

Answer 1

Work out the two x-intercepts and the midpoint of those two points will be the axis of symmetry.

Domain: Recognise that it is a parabola and that any x value you input is valid. Therefore the domain is all real numbers.

Range: Recognise that the function is an upside-down parabola. We can extract from the equation that it's maximum value is y=1. Therefore the range is \[\left\{ y:y \le1 \right\}\] and that y is real.