Question Graph the quadratic functions y = -2x2 and y = -2x2 + 4 on a separate piece of paper. Using those graphs, compare and contrast the shape and position of the graphs.

Answer 1

To graph the quadratic functions y = -2x^2 and y = -2x^2 + 4, we can first identify the vertex of the parabolas using the formula x = -b/2a.

For y = -2x^2, a = -2 and b = 0, so the vertex is at x = 0. Substituting x = 0 into the equation, we find the y-coordinate of the vertex to be y = 0.

For y = -2x^2 + 4, a = -2 and b = 0, so the vertex is also at x = 0. Substituting x = 0 into the equation, we find the y-coordinate of the vertex to be y = 4.

Now we can plot the vertex of each parabola and determine the shape of the curve. Since the coefficient of x^2 is negative in both equations, the parabolas will open downwards.

The graph of y = -2x^2 will be a downward-facing parabola with vertex at (0, 0), while the graph of y = -2x^2 + 4 will be a downward-facing parabola with vertex at (0, 4).

Comparing the two graphs:

- Both parabolas have the same shape, opening downwards.
- The graph of y = -2x^2 is below the x-axis and does not intersect the y-axis, while the graph of y = -2x^2 + 4 is shifted upwards by 4 units and intersects the y-axis at y = 4.

Overall, the two graphs are similar in shape but have different positions due to the vertical shift in the second equation.