Okay, so I'm asked to "Complete the table for each function".
1. f(x) = x^2
x = 0, +/-1, +/-2, +/-3
y = 0, 1, 4, 9
So, I plugged each of the x values into the equation and got the y values that are shown above? Are those correct, or did I do something wrong? We are also asked to graph the function. My problem is that when I graph it, it doesn't look like a parabola. I'm so confused.
There are two other tables that I was asked to fill out and graph. They don't make sense either.
2. g(x) = -2x^2
x = 0, +/-1, +/-2, +/-3
y = 0, -2, -8, -18
3. h(x) = 1/4x^2
x = 0, +/-1, +/-2, +/-3
y = 0, 1/4, 1. 2 1/4
You can get excellent graphing help at
http://rechneronline.de/function-graphs/
You can plot up to three functions at the same time, and set the x- and y- boundaries as desired.
I expect that you plotted the points wrong, if it didn't look like a parabola. Your tables look ok.
My problem was that I didn't understand that they wanted me to plot the positive AND the negative x values (hence why they labeled them +/-)to form the parabola. Thank you for your help!
To complete the table for each function and graph them correctly, you followed the correct steps. Let's go through each function one by one and address your concerns.
1. f(x) = x^2:
You correctly plugged in the given x values into the equation and obtained the corresponding y values. The table you provided is correct:
x = 0, +/-1, +/-2, +/-3
y = 0, 1, 4, 9
To graph this function, you can plot the points from the table on a coordinate plane. Since this is a quadratic function, the graph should form a parabola. However, it's important to note that the table you provided only includes a few x values, so you might not be seeing the full shape of the parabola. To get a better understanding of the graph, you can plot more points by choosing additional x values and calculating the corresponding y values. Once you have more points plotted, the parabolic shape should become clearer.
2. g(x) = -2x^2:
You correctly filled in the table with the given x values and obtained the corresponding y values:
x = 0, +/-1, +/-2, +/-3
y = 0, -2, -8, -18
This function is also a quadratic function, but in this case, the coefficient of x^2 is negative (-2). This means that the graph will open downwards. Therefore, when you plot the points from the table, they should align in a parabolic shape that faces downwards.
3. h(x) = 1/4x^2:
You again correctly filled in the table with the given x values and obtained the corresponding y values:
x = 0, +/-1, +/-2, +/-3
y = 0, 1/4, 1, 2 1/4
This function is also a quadratic function, but in this case, the coefficient of x^2 is positive (1/4). This means that the graph will open upwards, but it will be much broader and flatter compared to the previous examples. When you plot the points from the table, they should form a wider parabolic shape.
Remember, when graphing functions, it's crucial to include a sufficient number of points to accurately represent the shape of the graph. If you're only using a few points, the graph may appear distorted or incomplete.