Question 602·Easy·Math

0 / 2000

The $y$ -intercept of the graph of $y = \sqrt{x + 9}$ in the $xy$ -plane is $(0, y)$ . What is the value of $y$ ?

Your answer

An intercept is a point where a graph meets an axis. The $y$ -axis is vertical, so at a $y$ -intercept, $x=0$ . Put $0$ into the given rule, or define it in Desmos and evaluate at $0$ . If the question asks for $y$ , report the output. Setting $y=0$ finds an $x$ -intercept instead.

Hints

Hint 1
An intercept is a point where a graph meets an axis. Every point on the vertical $y$ -axis has a zero input. Which variable should you replace with $0$ in the given equation?
Hint 2
The square root symbol asks for the nonnegative number whose square is the number beneath it. After you use the zero input, what is beneath the radical, and what output does that give?

Step-by-step

Use the zero input
Step 1
Translate the intercept into an input
The $y$ -intercept is where the graph meets the vertical $y$ -axis. Its $x$ -coordinate is $0$ , matching the given $(0,y)$ , so put $0$ in for $x$ :
$y=\sqrt{0+9}=\sqrt9.$
Don't set $y=0$ ; that would find an $x$ -intercept.
Step 2
Evaluate the output
In Desmos, type $f(x)=\sqrt{x+9}$ to name the given rule, then type $f(0)$ to find its output at $x=0$ . Desmos prints $3$ . The square root is nonnegative, so $\sqrt9$ is $3$ , not $-3$ . The requested $y$ -coordinate is $3$ . Grid in 3.

Question 602·Easy·Math

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this