Answer:
No
Step-by-step explanation:
Quadratic functions with minimums, by default, have a domain of all real numbers (x∈R), this means any quadratic will lie in ≥ 2 quadrants (the positive left and right quadrant);
The only remaining question is it if lies in only these 2, a third as well or all 4 quadrants;
If the quadratic has no distinct solutions, this means it does not cross the x-axis, which means it is only above the x-axis and it will only therefore lie in the upper left and right quadrant;
If the quadratic has one solution, it would touch the x-axis but would not cross and enter either of the two quadrants below, therefore such a quadratic would only lie in the upper 2 quadrants;
If the quadratic has 2 distinct solutions, the graph must cross the x-axis falling into one or both of the quadrants below the x-axis;
Ultimately, the quadratic could have x-intercepts both to left of the y-axis, or both to the right or one to the left and one to the right;
In the case of both to one side, the portion of the function that lies under the x-axis will be in one of the lower quadrants, meaning the function will lie in 3 quadrants in total;
In the case of an x-intercept to the left and one to the right, then the portion of the function will lie in both negative quadrants under the y-axis, in which case the functions will occupy all 4 quadrants
So, the answer is no;
A quadratic function that has 2 distinct solutions will lie in either 3 or 4 quadrants, such a function cannot lie in only 2 quadratics.
