Additionally, the second graph has a vertex at (0,4), which means it is located 4 units higher on the y-axis compared to the vertex of the first graph. This upward shift of the second graph affects all the points on the graph, causing the entire parabola to move upward by 4 units.
The equation of the second graph, y = -2x^2 + 4, indicates that the coefficient of x^2 is -2, which means the parabola opens downward. The term "+4" in the equation indicates that the entire graph is shifted upward by 4 units compared to the first graph.
Both graphs will have the same shape and symmetry about the vertical line passing through the vertex, but the second graph will be located 4 units higher on the y-axis.
On the other hand, the graph of the quadratic function y = -2x^2 + 4 is also a downward-facing parabola opening downwards, but it is vertically shifted upward by 4 units. The vertex of this parabola is at (0,4).
In summary, both graphs have the same shape, which is a downward-facing parabola, but the second graph is vertically shifted 4 units upward compared to the first graph.
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