Find Y-Axis Intersection of y=(x+4)² Quadratic Function

Quadratic Functions with Y-Axis Intersection

Find the intersection of the function

y=(x+4)2 y=(x+4)^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 of the function with the Y-axis
00:03 At the intersection point with Y-axis X=0
00:06 Therefore, substitute X=0 and solve to find the intersection point with Y-axis
00:16 This is the Y value at the intersection point, substitute X=0 as we did at the point
00:25 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Find the intersection of the function

y=(x+4)2 y=(x+4)^2

With the Y

2

Step-by-step solution

To solve this problem, we will find the intersection of the function with the Y-axis by following these steps:

  • Step 1: Recognize that the intersection with the Y-axis occurs where x=0 x = 0 .
  • Step 2: Substitute x=0 x = 0 into the function y=(x+4)2 y = (x+4)^2 .
  • Step 3: Perform the calculation to find the y-coordinate.

Now, let's solve the problem:

Step 1: Identify the Y-axis intersection by setting x=0 x = 0 .
Step 2: Substitute x=0 x = 0 into the function:

y=(0+4)2=42=16 y = (0+4)^2 = 4^2 = 16

Step 3: The intersection point on the Y-axis is (0,16)(0, 16).

Therefore, the solution to the problem is (0,16)(0, 16).

3

Final Answer

(0,16) (0,16)

Key Points to Remember

Essential concepts to master this topic
  • Y-Axis Rule: Set x = 0 to find y-intercept
  • Technique: Substitute x = 0: y = (0+4)² = 16
  • Check: Point (0,16) lies on y-axis since x-coordinate is 0 ✓

Common Mistakes

Avoid these frequent errors
  • Confusing y-intercept with x-intercept
    Don't set y = 0 to find y-intercept = wrong axis! This gives you the x-intercept instead of the y-intercept. Always set x = 0 to find where the function crosses the y-axis.

Practice Quiz

Test your knowledge with interactive questions

Find the intersection of the function

\( y=(x-2)^2 \)

With the X

FAQ

Everything you need to know about this question

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

+

The y-axis is where x = 0 on the coordinate plane. Any point on the y-axis has an x-coordinate of 0, so we substitute x = 0 into the function to find the y-coordinate.

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

+

Y-intercept: Where the graph crosses the y-axis (set x = 0). X-intercept: Where the graph crosses the x-axis (set y = 0). They're completely different!

How do I write the y-intercept as a point?

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The y-intercept is always written as (0, y-value). Since we found y = 16 when x = 0, the point is (0,16) (0, 16) .

Why isn't the answer just 16?

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The question asks for the intersection point, not just the y-value. A point needs both coordinates: x and y. So the complete answer is the ordered pair (0,16) (0, 16) .

Can I check my answer by graphing?

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Yes! Graph y=(x+4)2 y = (x+4)^2 and look where it crosses the y-axis. You should see it crosses at y = 16, confirming your answer.

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