Question 136·Easy·Nonlinear Equations in One Variable; Systems in Two Variables
and .
What is the value of ?
For questions where a value of is given and is defined by a formula like , treat it as a straightforward substitution problem: replace with the given number, use parentheses around negative values, apply exponents before addition or subtraction, and then simplify step by step. Paying close attention to the negative sign and the order of operations will help you avoid common sign and squaring errors and let you answer quickly.
Hints
Identify what to do with x = -3
You are given a formula for in terms of and a specific value for . Think about what you should do with in the equation .
Be careful with the negative sign when squaring
When you substitute , make sure you put in parentheses before squaring. Ask yourself: what is ?
Finish the calculation
Once you know the value of when , substitute it back into the expression and perform the final addition.
Desmos Guide
Evaluate the expression directly
In a Desmos expression line, type (-3)^2 + 5 (with parentheses around -3). The numerical value that Desmos shows is the value of for .
Step-by-step Explanation
Substitute the given x-value into the equation
Start with the equation .
You are told that , so replace with :
Notice that the is in parentheses before squaring, so the negative sign is included in the square.
Square the negative number
Now evaluate .
Squaring means multiplying the number by itself:
Substitute this result back into the expression for :
Add the constant term
Compute the sum:
So the value of when is , which corresponds to answer choice C.