Which phrase describes the solution set for this function? f(x) = 2(x - 1)2 + 4
A.
one real solution and one complex solution
B.
two complex solutions
O C.
two real solutions
D.
one real solution

Note: The function is not an equation. I will form and solve an equation to answer the question.

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.

okay wait before i answer, is this for your points on a graph?

5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a=   -1/116