Question 136·Easy·Nonlinear Equations in One Variable; Systems in Two Variables

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$y = x^2 + 5$ and $x = -3$ .

What is the value of $y$ ?

A given input and a rule for $y$ signal function evaluation: put the input in place of $x$ to find the output. Write a negative input in parentheses before squaring it, because the sign is part of the number being squared. In Desmos, define the rule as a function and evaluate it at the given input.

Hints

Hint 1
A substitution replaces $x$ with the given input. Put the entire negative number in parentheses before applying the exponent. What expression do you get for $y$ ?
Hint 2
A square means multiplying a number by itself. Two negative factors make a positive product. What do you get when you multiply $-3$ by $-3$ ?

Step-by-step

Substitute, then evaluate
Step 1
Put the given input into the rule
The problem gives $x=-3$ , so substitute the whole input for $x$ :
$y=(-3)^2+5.$
Keep the parentheses: the square applies to $-3$ , not only to $3$ .
Step 2
Square the negative input
To square $-3$ , multiply it by itself:
$(-3)^2=(-3)(-3)=9.$
Two negative factors make a positive product. Using $3$ instead would give $3+5=8$ , but $3$ is not the square of $-3$ .
Step 3
Find the output in Desmos
Type $f(x)=x^2+5$ in Desmos, using $f$ as a name for the given rule. Then type $f(-3)$ . Desmos prints $14$ , which matches the positive square $9$ plus $5$ . So $y$ is $14$ when $x=-3$ . Square the whole negative input, including its sign. Choice C.

Question 136·Easy·Nonlinear Equations in One Variable; Systems in Two Variables

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this