Discover the Vertex of y=(x-1)²+3: A Parabola Challenge

Q: Why is the vertex (1,3) and not (-1,3)?

The tricky part is the sign! In vertex form $ y = a(x-h)^2 + k $, we see $ (x-1) $ which means h = 1, not -1. Think of it as 'x minus 1 equals zero when x = 1'.

Q: How do I remember which coordinate is which?

Use the pattern (h, k) where h comes from the $ (x-h) $ part and k is the number added at the end. So $ (x-1)^2 + 3 $ gives vertex $ (1, 3) $.

Q: What if the equation wasn't in vertex form?

You'd need to complete the square first! But this equation is already in perfect vertex form $ y = a(x-h)^2 + k $, so you can read the vertex directly.

Q: Does the coefficient 'a' affect the vertex location?

No! The coefficient 'a' only affects how wide or narrow the parabola is, and whether it opens up or down. The vertex position depends only on h and k values.

Vertex Form with Standard Parabola Structure

Find the vertex of the parabola

$y=(x-1)^2+3$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the vertex of the parabola

00:03 Use the formula to describe the parabolic function

00:10 The coordinates of the vertex are (P,K)

00:13 Use this formula and find the vertex point

00:16 Substitute appropriate values according to the given data

00:19 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 vertex of the parabola

$y=(x-1)^2+3$

Step-by-step solution

To find the vertex of the parabola described by the equation $y = (x-1)^2 + 3$ , we recognize that it is already in the vertex form $y = a(x-h)^2 + k$ .

Identify the components:

The expression $(x-1)$ indicates that $h = 1$ .
The constant term $+3$ indicates that $k = 3$ .

The vertex of the parabola is the point $(h, k)$ .

Therefore, the vertex of the given parabola is $(1, 3)$ .

Final Answer

$(1,3)$

Key Points to Remember

Essential concepts to master this topic

Vertex Form: Pattern $y = a(x-h)^2 + k$ gives vertex $(h,k)$
Technique: From $(x-1)^2$ get h=1, from +3 get k=3
Check: Substitute (1,3): $y = (1-1)^2 + 3 = 0 + 3 = 3$ ✓

Common Mistakes

Avoid these frequent errors

Confusing signs when reading h-value from vertex form
Don't read (x-1) as h = -1! This gives vertex (-1,3) instead of (1,3). The negative sign in (x-h) means h is positive when you see subtraction. Always remember: (x-1) means h = +1, while (x+1) would mean h = -1.

Practice Quiz

Test your knowledge with interactive questions

The following function has been graphed below:

$$ f(x)=x^2-6x $$

Calculate point C.

FAQ

Everything you need to know about this question

Why is the vertex (1,3) and not (-1,3)?

The tricky part is the sign! In vertex form $y = a(x-h)^2 + k$ , we see $(x-1)$ which means h = 1, not -1. Think of it as 'x minus 1 equals zero when x = 1'.

How do I remember which coordinate is which?

Use the pattern (h, k) where h comes from the $(x-h)$ part and k is the number added at the end. So $(x-1)^2 + 3$ gives vertex $(1, 3)$ .

What if the equation wasn't in vertex form?

You'd need to complete the square first! But this equation is already in perfect vertex form $y = a(x-h)^2 + k$ , so you can read the vertex directly.

Does the coefficient 'a' affect the vertex location?

No! The coefficient 'a' only affects how wide or narrow the parabola is, and whether it opens up or down. The vertex position depends only on h and k values.

How can I check if my vertex is correct?

Substitute your vertex coordinates back into the equation! At $(1,3)$ : $y = (1-1)^2 + 3 = 0 + 3 = 3$ . The y-coordinate matches, so it's correct!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 The Quadratic Function questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

Discover the Vertex of y=(x-1)²+3: A Parabola Challenge

Vertex Form with Standard Parabola Structure

❤️ 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 is the vertex (1,3) and not (-1,3)?

How do I remember which coordinate is which?

What if the equation wasn't in vertex form?

Does the coefficient 'a' affect the vertex location?

How can I check if my vertex is correct?

🌟 Unlock Your Math Potential

More Questions

Vertex Representation

Finding the Vertex of the Parabola: y = (x+3)² - 6

Find the Domain of y=-(x-4)²+1: Positive and Negative Analysis

Vertex Discovery: Analyzing the Quadratic y = (x-6)² + 1

Locate the Vertex in the Parabola y=(x-3)²

The Vertex of the Parabola

Find Point C on f(x)=x²-8x+16: Quadratic Function Graph Analysis

Calculate Point C on the Quadratic Graph of f(x)=x²-6x

Find the Vertex of y=(x+2)²-3: Parabola Analysis

Find the Vertex of y=(x-5)²+1: Parabola Analysis