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

Y-Axis Intersection with Quadratic Functions

Find the intersection of the function

y=(x2)2 y=(x-2)^2

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 function crosses the Y-axis.
00:12 Remember, at the Y-axis, X is always zero.
00:17 So, we'll substitute X equals zero into the equation to get the Y value.
00:26 This gives us the point where the function intersects the Y-axis.
00:33 And that's how we solve this 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=(x2)2 y=(x-2)^2

With the Y

2

Step-by-step solution

To determine the intersection of the function y=(x2)2 y = (x-2)^2 with the y-axis, we set x=0 x = 0 , as the y-axis is defined by all points where x=0 x = 0 .

Substituting x=0 x = 0 into the equation:

y=(02)2 y = (0 - 2)^2

Simplifying this expression:

y=(2)2=4 y = (-2)^2 = 4

Thus, the intersection point of the function with the y-axis is (0,4) (0, 4) .

Therefore, the solution to the problem is (0,4) (0, 4) .

3

Final Answer

(0,4) (0,4)

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 = (0-2)² = 4
  • Check: Point (0,4) lies on y-axis where x-coordinate is zero ✓

Common Mistakes

Avoid these frequent errors
  • Looking for x-intercept instead of y-intercept
    Don't set y = 0 when finding y-axis intersection = wrong axis! This finds where the graph crosses the x-axis, not the y-axis. Always set x = 0 to find where the function intersects 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 for every point! So to find where any function crosses the y-axis, you substitute x = 0 into the equation and solve for y.

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

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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). Don't mix them up!

How do I write the answer as a coordinate point?

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Always write intercepts as ordered pairs (x, y). For y-intercept, x = 0, so if y = 4, write (0,4) (0, 4) .

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

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No! Every function can have at most one y-intercept because each x-value can only give one y-value. But it can have multiple x-intercepts.

What if I get a negative result when I substitute?

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That's perfectly normal! Y-intercepts can be positive, negative, or zero. Just make sure your arithmetic is correct and write the coordinate point properly.

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