I'm graphing the parabola f(x)=x^2+2. I'm going to make a table of values, and I'm choosing 5 values. How do I know which value I should choose as my 3rd value so I can make the parabola symmetrical?
Never mind, I got it.
To make the parabola symmetrical, you need to choose a value that is equidistant from the other two values you have selected. For a quadratic function in standard form, such as f(x) = x^2 + 2, the vertex of the parabola represents its axis of symmetry.
To find the vertex, you can use the formula x = -b/2a, where a and b are the coefficients of x^2 and x, respectively. In this case, a = 1 and b = 0, so the vertex occurs at x = 0.
To make the parabola symmetrical, choose two values equidistant from the vertex. For example, you could choose x = -2 and x = 2 as your first and second values. Since these values are already symmetrical, the third value should be at the same distance on the other side of the vertex. So, you can choose x = -(-2) = 2 as your third value.
With these choices, your table of values could look like this:
```
x | f(x) = x^2 + 2
--------|-------------
-2 | 2
0 | 2
2 | 6
```
Remember to evaluate each value of x by substituting it into the function f(x) to find the corresponding y-values.