Find Y-Axis Intersection of y=(x-6)²: Quadratic Function Analysis

Y-Axis Intercepts with Vertex Form

Find the intersection of the function

y=(x6)2 y=(x-6)^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 the Y-axis, X = 0
00:07 Therefore, we substitute X = 0 and solve to find the intersection point with the Y-axis
00:21 This is the Y value at the intersection point, we substitute X=0 as we set at the point
00:28 And this is the solution to the problem

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=(x6)2 y=(x-6)^2

With the Y

2

Step-by-step solution

To find the intersection of the function y=(x6)2 y = (x-6)^2 with the y-axis, we follow these steps:

  • Step 1: Identify the known function and approach the problem by setting x=0 x = 0 since we are looking for the intersection with the y-axis.

  • Step 2: Substitute x=0 x = 0 into the equation y=(x6)2 y = (x-6)^2 .

  • Step 3: Perform the calculation to find y y .

Now, execute these steps:
Step 1: We are given the function y=(x6)2 y = (x-6)^2 .
Step 2: Substitute x=0 x = 0 into the equation:
y=(06)2 y = (0-6)^2
Step 3: Simplify the expression:
y=(6)2=36 y = (-6)^2 = 36

The point of intersection with the y-axis is therefore (0,36) (0, 36) .

Thus, the solution to the problem is (0,36) (0, 36) .

3

Final Answer

(0,36) (0,36)

Key Points to Remember

Essential concepts to master this topic
  • Y-Axis Rule: Set x = 0 to find where any function crosses y-axis
  • Technique: Substitute x = 0 into y = (x-6)² gives y = (-6)² = 36
  • Check: Y-intercept is always point (0, y-value), so answer is (0, 36) ✓

Common Mistakes

Avoid these frequent errors
  • Setting y = 0 instead of x = 0
    Don't set y = 0 to find y-intercept = you'll find x-intercepts instead! This confuses axes and gives completely wrong coordinates. Always set x = 0 when finding where the graph crosses the y-axis.

Practice Quiz

Test your knowledge with interactive questions

Find the intersection of the function

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

With the Y

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 coordinates (0, something), so we substitute x = 0 to find that 'something'!

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

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Y-intercept: Set x = 0, get point (0, y). X-intercept: Set y = 0, get point (x, 0). Don't mix these up - they're completely different!

Why isn't the answer (-6, 0)?

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That would be an x-intercept! The number -6 appears in the function y=(x6)2 y = (x-6)^2 , but it doesn't directly give us coordinates. We must calculate by substituting x = 0.

How do I remember which variable to set to zero?

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Think about the axis name: Y-intercept means the graph crosses the Y-axis. The Y-axis is where X = 0, so set x = 0 to find it!

Can a quadratic have more than one y-intercept?

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No! Every function can have at most one y-intercept because there's only one point where x = 0. However, quadratics can have 0, 1, or 2 x-intercepts.

What if I get a negative y-value?

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That's totally fine! Y-intercepts can be positive, negative, or zero. A negative y-value just means the graph crosses the y-axis below the x-axis.

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