Find Y-Axis Intersections: Solving x²+3-y=0

Q: Why do I substitute x = 0 to find the y-intercept?

The y-axis is where x = 0 for every point! Think of it like a vertical line through zero. Any point on this line has an x-coordinate of 0, so we substitute x = 0 to find the y-coordinate.

Q: How is this different from finding x-intercepts?

For x-intercepts, you set y = 0 and solve for x. For y-intercepts, you set x = 0 and solve for y. It's the opposite process!

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

No! A function can only cross the y-axis once. If it crossed twice, it wouldn't be a function anymore because one x-value would have two y-values.

Q: What if I get y = 0 as my answer?

That's fine! It means the y-intercept is at $ (0, 0) $, which is the origin. The function passes through the point where both axes meet.

Q: Do I always write the answer as a coordinate pair?

Yes! Y-intercepts are points on the graph, so they must be written as $ (0, y) $. Just saying "y = 3" isn't complete - you need the full coordinate $ (0, 3) $.

Y-Axis Intercepts with Quadratic Functions

At which points does the function $x^2+3-y=0$ 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 X-axis, Y equals 0

00:10 Substitute X=0 in our equation and solve to find the intersection point:

00:14 This is the value at the intersection point with the Y-axis

00:18 Isolate Y

00:25 This is the value at the intersection point with the Y-axis

00:30 X = 0 as we substituted at the beginning

00:33 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 $x^2+3-y=0$ intersect the y axis?

Step-by-step solution

To find where the function intersects the y-axis, we substitute $x = 0$ into the equation $x^2 + 3 - y = 0$ .

Substitute $x = 0$ into the function: $(0)^2 + 3 - y = 0$ .
Simplify: $0 + 3 - y = 0$ becomes $3 - y = 0$ .
Solving for $y$ , we get: $y = 3$ .

This means the function intersects the y-axis at the point $(0, 3)$ .

Therefore, the solution to the problem is $(0, 3)$ , corresponding to choice 3.

Final Answer

$(0,3)$

Key Points to Remember

Essential concepts to master this topic

Y-Intercept Rule: Set x = 0 to find where function crosses y-axis
Substitution Technique: Replace x with 0: (0)² + 3 - y = 0 becomes y = 3
Coordinate Check: Y-intercept is always (0, y-value), never (y-value, 0) ✓

Common Mistakes

Avoid these frequent errors

Writing the y-intercept with wrong coordinate order
Don't write the y-intercept as (3, 0) when y = 3! This gives the x-intercept format instead. Y-intercepts always have x = 0 first. Always write y-intercepts as (0, y-value).

Practice Quiz

Test your knowledge with interactive questions

Which chart represents the function $$ y=x^2-9 $$ ?

FAQ

Everything you need to know about this question

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

The y-axis is where x = 0 for every point! Think of it like a vertical line through zero. Any point on this line has an x-coordinate of 0, so we substitute x = 0 to find the y-coordinate.

How is this different from finding x-intercepts?

For x-intercepts, you set y = 0 and solve for x. For y-intercepts, you set x = 0 and solve for y. It's the opposite process!

Can a function have more than one y-intercept?

No! A function can only cross the y-axis once. If it crossed twice, it wouldn't be a function anymore because one x-value would have two y-values.

What if I get y = 0 as my answer?

That's fine! It means the y-intercept is at $(0, 0)$ , which is the origin. The function passes through the point where both axes meet.

Do I always write the answer as a coordinate pair?

Yes! Y-intercepts are points on the graph, so they must be written as $(0, y)$ . Just saying "y = 3" isn't complete - you need the full coordinate $(0, 3)$ .

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