Question
Compare and contrast y=-2x^2 and y=-2x^2+4
Answers
GPT 3.5
The two equations both have a quadratic shape, as they both have a leading coefficient of -2 and x^2 term. However, the second equation y=-2x^2+4 has an additional constant term of +4, which shifts the graph vertically upward by 4 units compared to y=-2x^2. So, the second equation has been translated 4 units upwards from the first equation.
Graphically, the two equations are identical in shape, curve downwards and open towards the negative direction, but the second equation is shifted upward by 4 units. Additionally, the vertex of the first equation y=-2x^2 is at (0,0) while the vertex of the second equation y=-2x^2+4 is at (0,4).
In summary, both equations have the same quadratic shape and leading coefficient, but the second equation y=-2x^2+4 has been shifted vertically upwards by 4 units compared to the first equation y=-2x^2.
Graphically, the two equations are identical in shape, curve downwards and open towards the negative direction, but the second equation is shifted upward by 4 units. Additionally, the vertex of the first equation y=-2x^2 is at (0,0) while the vertex of the second equation y=-2x^2+4 is at (0,4).
In summary, both equations have the same quadratic shape and leading coefficient, but the second equation y=-2x^2+4 has been shifted vertically upwards by 4 units compared to the first equation y=-2x^2.