Question 103·Easy·Nonlinear Functions
The function is defined by . What is the value of ?
(Express the answer as an integer)
For function-evaluation questions like this, immediately rewrite the function with the given input value in parentheses everywhere you see . Then simplify carefully, following the order of operations: powers first, then multiplication, then addition/subtraction. Pay extra attention to negative signs and squared negatives; always write substitutions like in parentheses to avoid sign errors.
Hints
Interpret the notation
means you should plug in for everywhere in the formula .
Use parentheses when substituting
Rewrite the expression with replaced by : wherever you see , write so you can handle the negative sign correctly.
Simplify carefully with negatives
Compute first, then multiply by 3, then handle the product , and finally add all the terms together.
Desmos Guide
Evaluate the function in Desmos
In Desmos, type 3(-1)^2 - 5(-1) + 2 exactly as written (with the parentheses). Press Enter and read the numerical result shown; that value is .
Step-by-step Explanation
Understand what means
The function is defined by .
The expression means: take the formula for and replace every with , then simplify.
Substitute into the function with parentheses
Write by substituting into the expression:
Using parentheses around helps keep track of signs, especially when squaring and multiplying.
Simplify step by step
First, evaluate the power: , so .
Next, multiply in the middle term: .
Now add all the terms:
So, .