Find Y-Intercept of y=(x-5)²: Quadratic Function Analysis

Q: Why do we set x = 0 to find the y-intercept?

The y-intercept is where the graph crosses the y-axis. On the y-axis, all points have x-coordinate = 0. So we substitute x = 0 to find the y-coordinate!

Q: Is (-5)² the same as -5²?

Yes! When we have $ (0-5)^2 $, this equals $ (-5)^2 $ which is 25. The negative sign is inside the parentheses, so it gets squared too: (-5) × (-5) = 25.

Q: Why isn't the answer (0,5)?

That would be true for $ y = x - 5 $, but our function is $ y = (x-5)^2 $. The square changes everything! When x = 0, we get (0-5)² = 25, not 5.

Q: How do I remember which coordinate goes first?

Think "x comes before y in the alphabet" so coordinates are always written as (x, y). For y-intercepts, x = 0, so the point is (0, y-value).

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

Y-intercept: Set x = 0, find y (where graph crosses y-axis)X-intercept: Set y = 0, find x (where graph crosses x-axis)Don't mix them up!

Q: Can I just look at the function to find the y-intercept?

For some functions yes, but it's safer to always substitute x = 0. This method works for every function and helps you avoid mistakes with more complex expressions.

Y-Intercept with Squared Expressions

Find the intersection of the function

$y=(x-5)^2$

With the Y

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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 =0

00:08 Therefore substitute X =0 and solve to find the intersection point with the Y-axis

00:23 This is the Y value at the intersection point, substitute X=0 as we did at the point

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

Find the intersection of the function

$y=(x-5)^2$

With the Y

Step-by-step solution

To find the intersection of the function $y = (x-5)^2$ with the y-axis, we follow these steps:

Step 1: Substitute $x = 0$ into the function to find the y-intercept.

Let's calculate:
- Substitute $x = 0$ into the function: $y = (0-5)^2$ .
- Simplifying further, $y = (-5)^2 = 25$ .

Thus, the intersection of the function $y = (x-5)^2$ with the y-axis occurs at the point $(0, 25)$ .

Therefore, the correct answer is $(0, 25)$ .

Final Answer

$(0,25)$

Key Points to Remember

Essential concepts to master this topic

Y-Intercept Rule: Set x = 0 and solve for y
Technique: Substitute x = 0: y = (0-5)² = (-5)² = 25
Check: Point (0,25) means when x is 0, y equals 25 ✓

Common Mistakes

Avoid these frequent errors

Confusing y-intercept with x-intercept
Don't set y = 0 to find the y-intercept = you'll get the x-intercept instead! This gives (5,0) which is completely wrong. Always set x = 0 when finding where the graph crosses 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 we set x = 0 to find the y-intercept?

The y-intercept is where the graph crosses the y-axis. On the y-axis, all points have x-coordinate = 0. So we substitute x = 0 to find the y-coordinate!

Is (-5)² the same as -5²?

Yes! When we have $(0-5)^2$ , this equals $(-5)^2$ which is 25. The negative sign is inside the parentheses, so it gets squared too: (-5) × (-5) = 25.

Why isn't the answer (0,5)?

That would be true for $y = x - 5$ , but our function is $y = (x-5)^2$ . The square changes everything! When x = 0, we get (0-5)² = 25, not 5.

How do I remember which coordinate goes first?

Think "x comes before y in the alphabet" so coordinates are always written as (x, y). For y-intercepts, x = 0, so the point is (0, y-value).

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

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

Don't mix them up!

Can I just look at the function to find the y-intercept?

For some functions yes, but it's safer to always substitute x = 0. This method works for every function and helps you avoid mistakes with more complex expressions.

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Find Y-Intercept of y=(x-5)²: Quadratic Function Analysis

Y-Intercept with Squared Expressions

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do we set x = 0 to find the y-intercept?

Is (-5)² the same as -5²?

Why isn't the answer (0,5)?

How do I remember which coordinate goes first?

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

Can I just look at the function to find the y-intercept?

🌟 Unlock Your Math Potential

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