Find Y-Axis Intersection: Solving y=(x+5)²+2 Quadratic Function

Q: What's the difference between x-intercept and y-intercept?

The y-intercept is where the graph crosses the y-axis (set x = 0). The x-intercept is where it crosses the x-axis (set y = 0). They're completely different points!

Q: Why do we set x = 0 for y-intercept?

The y-axis is the vertical line where x = 0. Any point on this line has x-coordinate of 0, so we substitute x = 0 to find the y-coordinate.

Q: How do I expand (x+5)² when x = 0?

When x = 0, you get $ (0+5)^2 = 5^2 = 25 $. Then add 2 to get 27. No need to expand the full binomial!

Q: Can a quadratic function have more than one y-intercept?

No! Every function can have at most one y-intercept because there's only one point where x = 0. But it can have zero, one, or two x-intercepts.

Y-Axis Intercepts with Vertex Form

Find the intersection of the function

$y=(x+5)^2+2$

With the Y

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the intersection point with the Y-axis

00:03 Substitute X=0 and solve to find the intersection point

00:13 Let's calculate

00:27 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Find the intersection of the function

$y=(x+5)^2+2$

With the Y

Step-by-step solution

To find the intersection of the function $y = (x+5)^2 + 2$ with the y-axis, we follow these steps:

Step 1: Identify that the intersection with the y-axis occurs when $x = 0$ .
Step 2: Substitute $x = 0$ into the equation $y = (x+5)^2 + 2$ .
Step 3: Perform the substitution and simplify: $y = (0+5)^2 + 2$ .
Step 4: Simplify further: $y = 5^2 + 2 = 25 + 2 = 27$ .

Thus, the intersection point with the y-axis is $(0, 27)$ .

The correct answer is option 4: $(0, 27)$ .

Final Answer

$(0,27)$

Key Points to Remember

Essential concepts to master this topic

Rule: Y-axis intersection occurs when x equals zero
Technique: Substitute x = 0: (0+5)² + 2 = 27
Check: Point (0,27) means y-value is 27 when x is 0 ✓

Common Mistakes

Avoid these frequent errors

Looking for x-intercept instead of y-intercept
Don't set y = 0 to find y-intercept = gives x-intercepts instead! This confuses which axis you're finding. Always set x = 0 to find where the graph crosses the y-axis.

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

What's the difference between x-intercept and y-intercept?

The y-intercept is where the graph crosses the y-axis (set x = 0). The x-intercept is where it crosses the x-axis (set y = 0). They're completely different points!

Why do we set x = 0 for y-intercept?

The y-axis is the vertical line where x = 0. Any point on this line has x-coordinate of 0, so we substitute x = 0 to find the y-coordinate.

How do I expand (x+5)² when x = 0?

When x = 0, you get $(0+5)^2 = 5^2 = 25$ . Then add 2 to get 27. No need to expand the full binomial!

What if I got (27,0) as my answer?

That's backwards! Remember: y-intercept points are written as (0, y-value). The x-coordinate is always 0, and 27 is the y-coordinate, so it's (0,27).

Can a quadratic function have more than one y-intercept?

No! Every function can have at most one y-intercept because there's only one point where x = 0. But it can have zero, one, or two x-intercepts.

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