Two parabolas: f(x) opens upward and passes through origin. g(x) is shifted right 3 units and up 4 units, intersecting at (-2,4) and (4,4). Jack's equation likely relates f(x) shifted right and up to g(x).
The graph you sent me shows the functions f(x) =
and g(x) =
+ 4. The function f(x) =
is a parabola that opens upwards and passes through the origin. The function g(x) =
+ 4 is also a parabola that opens upwards, but it is shifted 3 units to the right and 4 units up compared to the function f(x) =
The points of intersection between the two parabolas are the solutions to the equation f(x) = g(x). In this case, the points of intersection are (-2, 4) and (4, 4).
To find the equation that Jack was solving, we need to look at the relationship between the two parabolas. We can see that the function g(x) is the result of taking the function f(x) and shifting it 3 units to the right and 4 units up. This means that the equation that Jack was solving is most likely of the form f(x + h) + k = g(x), where h and k are constants.
We can plug the points of intersection into this equation to solve for h and k. For example, if we plug the point (-2, 4) into the equation, we get:
f(-2 + h) + k = g(-2)
4 + k = 4
k = 0
We can do the same thing with the point (4, 4) and get the same answer for k. Therefore, the equation that Jack was solving is most likely f(x + 3) = g(x).