Finding Y-Intercept: Substituting x=0 into Equations

Q: Why do we substitute x = 0 specifically?

The y-axis is the vertical line where x always equals 0. To find where any graph crosses this line, we need to see what happens when $ x = 0 $.

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

Y-intercept: Set x = 0, solve for y (crosses y-axis)X-intercept: Set y = 0, solve for x (crosses x-axis)

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

No! A function can only cross the y-axis once because each x-value has exactly one y-value. However, it can have multiple x-intercepts.

Q: How do I write the y-intercept as a coordinate?

Always write it as (0, y-value). In this example, if $ y = p^2 $, then the y-intercept point is $ (0, p^2) $.

Y-Intercept with Coordinate Substitution

To find the y axis intercept, you substitute $x=0$ into the equation and solve for y.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 To find the intersection point with the Y-axis, we substitute X = 0?

00:03 Let's draw any parabola that intersects with the Y-axis

00:21 This is the line where X = 0 (Y-axis)

00:25 Therefore, to find the intersection point with the Y-axis, we substitute X = 0

00:28 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

To find the y axis intercept, you substitute $x=0$ into the equation and solve for y.

Step-by-step solution

To determine if the given statement is true, consider the equation of the parabola $y = (x - p)^2$ . The y-intercept occurs where the parabola crosses the y-axis, which is at $x = 0$ .

Step 1: Substitute $x = 0$ into the equation:

$y = (0 - p)^2 = p^2$

Step 2: Calculate the y-intercept:

The y-intercept of the parabola is $y = p^2$ .

Conclusion: The statement "To find the y-axis intercept, you substitute $x = 0$ into the equation and solve for $y$ " is indeed True, as applying this method correctly determined the y-intercept for the given form of a parabola. Therefore, the answer to the problem is True.

Final Answer

True

Key Points to Remember

Essential concepts to master this topic

Definition: Y-intercept occurs where graph crosses y-axis at x = 0
Method: Replace x with 0: y = (0 - p)² = p²
Verify: Point (0, p²) should lie on the original graph ✓

Common Mistakes

Avoid these frequent errors

Substituting y = 0 instead of x = 0
Don't set y = 0 to find y-intercept = this finds x-intercept instead! Students confuse which variable to substitute as zero. Always substitute x = 0 to find 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 we substitute x = 0 specifically?

The y-axis is the vertical line where x always equals 0. To find where any graph crosses this line, we need to see what happens when $x = 0$ .

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

Y-intercept: Set x = 0, solve for y (crosses y-axis)
X-intercept: Set y = 0, solve for x (crosses x-axis)

Can a function have more than one y-intercept?

No! A function can only cross the y-axis once because each x-value has exactly one y-value. However, it can have multiple x-intercepts.

What if I get a negative y-intercept?

That's completely normal! A negative y-intercept just means the graph crosses the y-axis below the x-axis. For example, if y = -4, the point is (0, -4).

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

Always write it as (0, y-value). In this example, if $y = p^2$ , then the y-intercept point is $(0, p^2)$ .

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