Solving x²+y=3: Finding Y-Axis Intersection Points

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

The y-axis is the vertical line where every point has an x-coordinate of 0. So to find where any graph crosses the y-axis, we substitute x = 0 into the equation.

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

For y-axis intersections, set x = 0 and solve for y. For x-axis intersections, set y = 0 and solve for x. Don't mix these up!

Q: Can a function have more than one y-axis intersection?

No! A function can only cross the y-axis once. If it crossed twice, it wouldn't pass the vertical line test and wouldn't be a function.

Q: How do I write the intersection point correctly?

Always write points as (x, y) coordinates. For y-axis intersections, the x-coordinate is always 0, so the format is (0, y-value).

Q: What if I get a negative y-value?

That's perfectly normal! The y-axis extends both above and below the origin. Negative y-values just mean the intersection point is below the x-axis.

Y-Axis Intersections with Quadratic Relations

At which points does the function $x^2+y=3$

intersect the y axis?

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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 equals 0

00:07 Let's substitute X=0 in our equation and solve to find the intersection point:

00:16 This is the value at the intersection point with the Y-axis

00:19 X = 0 as we substituted initially

00:24 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

At which points does the function $x^2+y=3$

intersect the y axis?

Step-by-step solution

To solve this problem and determine where the function $x^2 + y = 3$ intersects the y-axis, we follow these steps:

Step 1: Since the y-axis is where the x-coordinate is zero, set $x = 0$ in the given equation.
Step 2: Substitute $x = 0$ into the equation $x^2 + y = 3$ , which simplifies to $0 + y = 3$ .
Step 3: From the simplified equation, solve for $y$ . The result is $y = 3$ .

This indicates that the point of intersection on the y-axis is $(0, 3)$ .

Accordingly, the solution to the problem is that the graph intersects the y-axis at the point $(0, 3)$ .

Final Answer

$(0,3)$

Key Points to Remember

Essential concepts to master this topic

Y-Axis Rule: Set x = 0 to find y-axis intersection points
Technique: Substitute $x = 0$ into $x^2 + y = 3$ gives $y = 3$
Check: Point (0,3) satisfies original equation: $0^2 + 3 = 3$ ✓

Common Mistakes

Avoid these frequent errors

Using wrong coordinate for y-axis intersection
Don't set y = 0 to find y-axis intersections = gives x-axis points instead! The y-axis is where x-coordinates are zero, not y-coordinates. Always set x = 0 when finding where graphs cross the y-axis.

Practice Quiz

Test your knowledge with interactive questions

Find the ascending area of the function

$$ f(x)=2x^2 $$

FAQ

Everything you need to know about this question

Why do we set x = 0 for y-axis intersections?

The y-axis is the vertical line where every point has an x-coordinate of 0. So to find where any graph crosses the y-axis, we substitute x = 0 into the equation.

What's the difference between x-axis and y-axis intersections?

For y-axis intersections, set x = 0 and solve for y. For x-axis intersections, set y = 0 and solve for x. Don't mix these up!

Can a function have more than one y-axis intersection?

No! A function can only cross the y-axis once. If it crossed twice, it wouldn't pass the vertical line test and wouldn't be a function.

How do I write the intersection point correctly?

Always write points as (x, y) coordinates. For y-axis intersections, the x-coordinate is always 0, so the format is (0, y-value).

What if I get a negative y-value?

That's perfectly normal! The y-axis extends both above and below the origin. Negative y-values just mean the intersection point is below the x-axis.

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