Final answer:
An example of a quadratic function with two real solutions with a multiplicity of 2 is f(x) = (x - 2)², which yields the solution x = 2. Since this is a perfect square, the graph touches the x-axis at x = 2 but does not cross it, confirming the multiplicity.
Step-by-step explanation:
To find a quadratic function that has two real solutions, each with a multiplicity of 2, we need to look for a function that will touch the x-axis at one point and not cross it. This occurs when the function is a perfect square trinomial. An example would be:
A. f(x) = (x - 2)2, solutions: x = 2 (multiplicity 2)
To solve for the solutions algebraically, we set the function equal to zero:
0 = (x - 2)2
We then take the square root of both sides:
±√0 = x - 2
Since the square root of 0 is 0, this simplifies to:
0 = x - 2
Adding 2 to both sides gives us the solution:
x = 2
Since this is the only solution we obtained, and we arrived at it by solving a perfect square, this solution indeed has a multiplicity of 2, which means the graph of the function touches the x-axis at this point but does not cross it.