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. (3 points)

henry bruh i dont understand any of that

Y = -2x^2

h = Xv = -B/2A = 0/-4 = 0.
k = -2*0^2 = 0.
V(0,0).

Use the following points for graphing:

Y = -2x^2.

(x,y)
(-2,-8)
(-1,-2)
V(0,0)
(1,-2)
(2,-8)

Y = -2x^2 + 4.

h = Xv = -B/2A = 0/-4 = 0.
k = Yv = -2*0^2 + 4 = 4.
V(0,4).

(-2,-4)
(-1,2)
V(0,4)
(1,2)
(2,-4)

It's Bigger Than Black And White!

To graph the quadratic functions y = -2x^2 and y = -2x^2 + 4, you can follow these steps:

1. Plotting the vertex:
The vertex of a quadratic function is given by the formula (-b/2a, f(-b/2a)), where a, b, and c are coefficients of the quadratic equation in the form ax^2 + bx + c = 0.
For the functions y = -2x^2 and y = -2x^2 + 4, the value of a is -2. Therefore, the x-coordinate of the vertex is (-(-b/2a)).
For both functions, b = 0. Hence, the x-coordinate of the vertex is 0.
To find the y-coordinate of the vertex, substitute the x-value into the equation. For y = -2x^2, f(-b/2a) = -2(0^2) = 0.
For the second function, y = -2x^2 + 4, f(-b/2a) = -2(0^2) + 4 = 4.
So, the vertex for both functions is (0, 0) and (0, 4), respectively.

2. Finding the y-intercept:
To find the y-intercept, substitute x = 0 into the equation and solve for y.
For y = -2x^2, the y-intercept is found by substituting x = 0, which gives y = -2(0^2) = 0.
For y = -2x^2 + 4, substituting x = 0 gives y = -2(0^2) + 4 = 4.
The y-intercepts for both functions are (0, 0) and (0, 4) respectively.

3. Plotting additional points:
Choose some x-values to find the corresponding y-values. This will help you plot more points and get a clear picture of the shape of the quadratic functions.
For y = -2x^2:
Let's choose x = -1, x = 1, and x = 2.
When x = -1, y = -2(-1)^2 = -2.
When x = 1, y = -2(1)^2 = -2.
When x = 2, y = -2(2)^2 = -8.
So, we have the points (-1, -2), (1, -2), and (2, -8).

For y = -2x^2 + 4:
Using the same x-values chosen earlier, let's find the corresponding y-values.
When x = -1, y = -2(-1)^2 + 4 = 6.
When x = 1, y = -2(1)^2 + 4 = 2.
When x = 2, y = -2(2)^2 + 4 = -4.
So, we have the points (-1, 6), (1, 2), and (2, -4).

4. Plotting the points and drawing the graph:
Now, plot the vertex, y-intercept, and the additional points on a graph paper.
For y = -2x^2, the graph is a downward-facing parabola with the vertex at (0, 0) and passes through (-1, -2), (1, -2), and (2, -8).

For y = -2x^2 + 4, the graph is also a downward-facing parabola with the vertex at (0, 4) and passes through (-1, 6), (1, 2), and (2, -4).

On the separate piece of paper, draw the graphs of both functions using the information discussed above. Label each graph with its corresponding function to avoid confusion.

Comparing and contrasting the shape and position of the graphs:
1. Shape:
Both graphs have the same shape, which is a downward-facing parabola. This is because the coefficient of x^2 in both functions is -2.
2. Position:
The positions of the graphs differ in the y-direction. The graph of y = -2x^2 + 4 is shifted upward by 4 units compared to y = -2x^2. This shift is evident from the position of their respective vertices. The vertex (0, 0) for y = -2x^2 is at the origin, while the vertex (0, 4) for y = -2x^2 + 4 is above the x-axis at y = 4.
Thus, the graphs are similar in shape but differ in their vertical positions.