Find Y-Intercept of (x+2)²+3: Quadratic Function Analysis

Q: Why do I set x = 0 to find the y-intercept?

The y-intercept is where the graph crosses the y-axis. On the y-axis, all points have an x-coordinate of 0, so we substitute $ x = 0 $ into the function.

Q: What's the difference between (0,7) and (7,0)?

(0,7) means x=0 and y=7, which is the y-intercept. (7,0) means x=7 and y=0, which would be an x-intercept. The order matters: (x-coordinate, y-coordinate).

Q: How do I expand (x+2)² step by step?

When x=0: $ (0+2)^2 = 2^2 = 2 \times 2 = 4 $. Then add 3: $ 4 + 3 = 7 $. You don't need to fully expand the binomial for y-intercepts!

Q: Can I just read the y-intercept from vertex form?

Not directly! While $ y = (x+2)^2 + 3 $ tells us the vertex is at (-2, 3), you still need to substitute x = 0 to find where it crosses the y-axis.

Y-intercept Finding with Vertex Form

Find the intersection of the function

$y=(x+2)^2+3$

With the Y

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's find where the line crosses the Y-axis.

00:12 We do this by setting X to zero. Then solve the equation.

00:18 Alright, let's work it out together.

00:31 And there you go, that's how we solve this problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Find the intersection of the function

$y=(x+2)^2+3$

With the Y

Step-by-step solution

To solve the problem of finding the intersection of the function $y = (x+2)^2 + 3$ with the Y-axis, we will follow these steps:

Let's begin with identifying the point where the function intersects the Y-axis. A point on the Y-axis always has $x = 0$ . So, we’ll substitute this value into the function to find the corresponding y-coordinate.

Substitute $x = 0$ into the function:

$y = (0+2)^2 + 3$

First, calculate $(0+2)^2$ :

$(0+2)^2 = 2^2 = 4$

Then add 3 to the result:

$y = 4 + 3 = 7$

Thus, the intersection point on the Y-axis is $(0, 7)$ .

Therefore, the solution to the problem is $(0, 7)$ .

Final Answer

$(0,7)$

Key Points to Remember

Essential concepts to master this topic

Y-intercept Rule: Set x = 0 to find where function crosses y-axis
Technique: Substitute: y = (0+2)² + 3 = 4 + 3 = 7
Check: Y-intercept is always point (0, y-value) giving (0, 7) ✓

Common Mistakes

Avoid these frequent errors

Confusing x-intercept and y-intercept
Don't set y = 0 to find y-intercept = gives x-intercept instead! Students often mix up which variable to set to zero. Always set x = 0 to find y-intercept and y = 0 to find x-intercept.

Practice Quiz

Test your knowledge with interactive questions

Find the corresponding algebraic representation of the drawing:

FAQ

Everything you need to know about this question

Why do I set x = 0 to find the y-intercept?

The y-intercept is where the graph crosses the y-axis. On the y-axis, all points have an x-coordinate of 0, so we substitute $x = 0$ into the function.

What's the difference between (0,7) and (7,0)?

(0,7) means x=0 and y=7, which is the y-intercept. (7,0) means x=7 and y=0, which would be an x-intercept. The order matters: (x-coordinate, y-coordinate).

How do I expand (x+2)² step by step?

When x=0: $(0+2)^2 = 2^2 = 2 \times 2 = 4$ . Then add 3: $4 + 3 = 7$ . You don't need to fully expand the binomial for y-intercepts!

Can I just read the y-intercept from vertex form?

Not directly! While $y = (x+2)^2 + 3$ tells us the vertex is at (-2, 3), you still need to substitute x = 0 to find where it crosses the y-axis.

What if I got a negative y-intercept?

That's totally fine! Y-intercepts can be positive, negative, or zero. Just make sure your arithmetic is correct when substituting $x = 0$ .

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