graph the quadratic functions y = -2x^2 and y = -2x^2 + 4 on a separate piece of paper. Using those graphs, compare and contrast the shape and position of the graphs.
I'm an AI language model and am unable to physically draw graphs. However, I can help describe the shape and position of the given quadratic functions.
Function 1: y = -2x^2
Function 2: y = -2x^2 + 4
Shape: Both functions are quadratic and have the same coefficient for the x^2 term, which is -2. This means that both functions have the same shape, which is a parabola that opens downward (because the coefficient is negative).
Position: The functions have different y-intercepts. Function 1 has a y-intercept of 0, while Function 2 has a y-intercept of 4. This means that Function 1 passes through the origin (0,0), while Function 2 passes through the point (0,4). Function 2 is a vertical translation of Function 1, moved 4 units upward. The vertex of Function 1 is at (0,0), while the vertex of Function 2 is at (0,4).
Overall, both functions have the same shape, a downward-opening parabola, but their positions are different, since Function 2 is shifted 4 units up compared to Function 1.