Question 124·Easy·Nonlinear Functions
The quadratic function is defined by . What is the value of ?
(Express the answer as an integer)
For function-evaluation questions, ignore any urge to "interpret" the function and instead directly substitute the given input for in the formula. Then follow the order of operations carefully: simplify inside parentheses, apply exponents, and only then add or subtract. Writing out each intermediate step (like , then , then the final subtraction) helps avoid small but costly arithmetic mistakes on the SAT.
Hints
Focus on what g(0) asks for
Look at the definition . To find , what number should you substitute everywhere you see ?
Work step by step
After you substitute , simplify the expression inside the parentheses first, then apply the exponent, and finally do the subtraction.
Be careful with the square and the subtraction
Make sure you square the entire quantity before subtracting 5. Do not subtract 5 until after you have found the value of .
Desmos Guide
Enter the function
In Desmos, type the function exactly as given: g(x) = (x + 3)^2 - 5. This defines so you can evaluate it at specific -values.
Evaluate g(0)
On a new line in Desmos, type g(0) and look at the numeric output Desmos gives. That value is the answer for .
Step-by-step Explanation
Understand what g(0) means
The notation means "the value of the function when ." So you should take the formula for and replace every with .
The function is defined as
So will be
Simplify inside the parentheses and apply the exponent
First, simplify the expression inside the parentheses:
Next, evaluate the square:
so now you have
Finish the subtraction to find g(0)
Subtract 5 from 9:
Therefore,
So the value you should enter is 4.