Note: The function is not an equation. I will form and solve an equation to answer the question.
Answer:
C. Two real solutions
Step-by-step explanation:
We have the following function:
f(x)=2(x-1)^2+4
It does not form an equation to solve, and therefore, there are no 'solutions'. We must equate the function to something to set a condition and solve it. We'll complete the equation.
Solve for x when:
f(x)=12
Substituting the function:
2(x-1)^2+4=12
Subtracting 4:
2(x-1)^2=8
Dividing by 2:
(x-1)^2=4
Taking square root:
x-1=\pm\sqrt{4}
Solving:
x=1\pm2
We have two real solutions x=3 and x=-1
Note if we had equated to 4, then the equation would have had only one real solution, and if we had equated to 0, we would have two complex solutions.
