Find Y-Axis Intersection: Solving y=(x-3)²-4 Quadratic Function

Q: 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, y). So to find where your function crosses the y-axis, substitute x = 0!

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

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

Q: Why is the answer (0,5) and not just 5?

The y-intercept is a point on the coordinate plane! It needs both coordinates: (x,y) = (0,5). The number 5 alone is just the y-coordinate.

Q: Does every function have exactly one y-intercept?

Yes! Every function passes the vertical line test, so it can only cross the y-axis (the line x = 0) at most once. Most functions have exactly one y-intercept.

Q: How do I check if (0,5) is correct?

Substitute back: $ y = (0-3)^2 - 4 = (-3)^2 - 4 = 9 - 4 = 5 $. Since we get y = 5 when x = 0, the point (0,5) is correct!

Y-Intercept Finding with Vertex Form

Find the intersection of the function

$y=(x-3)^2-4$

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 line crosses the Y-axis.

00:12 Set X equals zero, and solve the equation to discover the point.

00:19 Now, let's calculate it together.

00:28 And here we have our solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Find the intersection of the function

$y=(x-3)^2-4$

With the Y

Step-by-step solution

The problem asks us to find where the parabola given by $y = (x-3)^2 - 4$ intersects the y-axis. The intersection with the y-axis occurs where $x = 0$ . Let's find the value of $y$ by substituting $x = 0$ into the equation:

$y = (0 - 3)^2 - 4$

Simplify inside the parentheses:

$y = (-3)^2 - 4$

Calculate $(-3)^2$ :

$y = 9 - 4$

Subtract 4 from 9:

$y = 5$

Thus, the intersection of the function with the y-axis occurs at the point $(0, 5)$ .

The correct answer from the choices provided is $(0,5)$ .

Final Answer

$(0,5)$

Key Points to Remember

Essential concepts to master this topic

Y-Intercept Rule: Set x = 0 to find where curve meets y-axis
Substitution: Replace x with 0: (0-3)² - 4 = 9 - 4 = 5
Check: Point (0,5) means when x = 0, y = 5 ✓

Common Mistakes

Avoid these frequent errors

Setting y = 0 instead of x = 0
Don't set y = 0 to find y-intercept = this finds x-intercepts instead! This gives you where the parabola crosses the x-axis, not the y-axis. Always set x = 0 to find the y-intercept.

Practice Quiz

Test your knowledge with interactive questions

Which equation represents the function:

$$ y=x^2 $$

moved 2 spaces to the right

and 5 spaces upwards.

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, y). So to find where your function crosses the y-axis, substitute x = 0!

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

Y-intercept: Set x = 0, find y-value (where curve crosses y-axis)

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

Why is the answer (0,5) and not just 5?

The y-intercept is a point on the coordinate plane! It needs both coordinates: (x,y) = (0,5). The number 5 alone is just the y-coordinate.

Does every function have exactly one y-intercept?

Yes! Every function passes the vertical line test, so it can only cross the y-axis (the line x = 0) at most once. Most functions have exactly one y-intercept.

How do I check if (0,5) is correct?

Substitute back: $y = (0-3)^2 - 4 = (-3)^2 - 4 = 9 - 4 = 5$ . Since we get y = 5 when x = 0, the point (0,5) is correct!

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