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.
Hey, let's calm here. I know, stressing about school sucks and I did the same as all of you- Luckily, I graphed it on Desmos (which you can always use if youre stuck on a graph question, its a site online!!) and here's the answer i got:
PARAPHRASE THE FOLLOWING:
The first equation has a vertex at (0, 0). Adding 4 to the end of the equation causes the y value to do the same, moving the vertex up by 4. This means the vertex is now at (0, 4). This changes all known points on the function, as they will all be slightly positioned around the first function.
learn how to spell first anonymouse
you guys aren't helping
thanks soooo much every1!! :3
thx
I would suggest you graph the two functions on the same grid, not on separate pieces of paper.
You will be able to answer the questions so much easier.
Make a table of values for each one, I suggest you use the same values of x for each one.
there are many handy online graphing sites that you can use.
Thank you @Mori<3
To graph the quadratic functions y = -2x^2 and y = -2x^2 + 4, follow these steps:
1. Draw a set of coordinate axes on a piece of paper, with a horizontal x-axis and a vertical y-axis.
2. Plot the points of the first equation y = -2x^2. To do this, substitute different x-values into the equation and determine the corresponding y-values. For example:
- For x = -2, y = -2(-2)^2 = -2(4) = -8
- For x = -1, y = -2(-1)^2 = -2(1) = -2
- For x = 0, y = -2(0)^2 = -2(0) = 0
- For x = 1, y = -2(1)^2 = -2(1) = -2
- For x = 2, y = -2(2)^2 = -2(4) = -8
Plot these points (-2, -8), (-1, -2), (0, 0), (1, -2), and (2, -8) on the graph. Connect the points with a smooth curve. This curve represents the graph of y = -2x^2.
3. Plot the points of the second equation y = -2x^2 + 4. Repeat the process described above, but this time, include the constant term (+4) in the equation to determine the y-values. For example:
- For x = -2, y = -2(-2)^2 + 4 = -2(4) + 4 = -8 + 4 = -4
- For x = -1, y = -2(-1)^2 + 4 = -2(1) + 4 = -2 + 4 = 2
- For x = 0, y = -2(0)^2 + 4 = -2(0) + 4 = 4
- For x = 1, y = -2(1)^2 + 4 = -2(1) + 4 = -2 + 4 = 2
- For x = 2, y = -2(2)^2 + 4 = -2(4) + 4 = -8 + 4 = -4
Plot these points (-2, -4), (-1, 2), (0, 4), (1, 2), and (2, -4) on the graph. Connect the points with a smooth curve. This curve represents the graph of y = -2x^2 + 4.
Now let's compare and contrast the shape and position of the graphs:
- Shape: Both graphs are quadratic, meaning they are parabolas. In both cases, the coefficient of x^2 is negative (-2), which indicates that the parabolas open downward.
- Position: The first graph y = -2x^2 intersects the y-axis at the origin (0, 0), while the second graph y = -2x^2 + 4 intersects the y-axis at (0, 4). This means that the second graph is shifted upward by 4 units compared to the first graph. Other than this vertical shift, both graphs have the same shape and open downward.
Don't be rude.
It's really easy to graph things online, and in case you haven't noticed, you can't send images on Jishka.
Maybe try putting effort into your work for once, and be grateful that someone tried helping you.