To determine the coordinates of points A, B, C, and D on the graphs of the functions f(x) = 2x^2 + 8 and g(x) = 3x + 6, we need to substitute different values of x into the equations and calculate the corresponding y-values. Here's how we can do that:
1. For function f(x) = 2x^2 + 8:
- Choose a value for x, let's say x = 0.
- Substitute x = 0 into the equation: f(0) = 2(0)^2 + 8 = 8.
- So, the coordinate of point A is (0, 8).
2. For function g(x) = 3x + 6:
- Choose a value for x, let's say x = 0.
- Substitute x = 0 into the equation: g(0) = 3(0) + 6 = 6.
- So, the coordinate of point B is (0, 6).
Now, let's choose another value for x, let's say x = 2, and calculate the corresponding y-values:
3. For function f(x) = 2x^2 + 8:
- Substitute x = 2 into the equation: f(2) = 2(2)^2 + 8 = 2(4) + 8 = 16 + 8 = 24.
- So, the coordinate of point C is (2, 24).
4. For function g(x) = 3x + 6:
- Substitute x = 2 into the equation: g(2) = 3(2) + 6 = 6 + 6 = 12.
- So, the coordinate of point D is (2, 12).
In summary, the coordinates of points A, B, C, and D on the graphs of the functions f(x) = 2x^2 + 8 and g(x) = 3x + 6 are as follows:
- Point A: (0, 8)
- Point B: (0, 6)
- Point C: (2, 24)
- Point D: (2, 12)
These coordinates represent the points where the graphs of the functions intersect the x and y axes.