Locate the Vertex of the Parabola: y = (x-6)² + 1

Q: Why is the vertex (6,1) and not (-6,1)?

This is the most common mistake! In vertex form $ y = (x-h)^2 + k $, when you see (x-6), the h-value is positive 6, not negative 6. Think of it as x minus 6 equals zero when x = 6.

Q: How do I remember which number is h and which is k?

Easy trick: h is the number inside the parentheses (affects x-coordinate), and k is the number outside the parentheses (affects y-coordinate). So in $ (x-6)^2 + 1 $, h = 6 and k = 1.

Q: What if the equation was y = (x+6)² + 1 instead?

Then the vertex would be (-6, 1)! When you see (x+6), that's the same as (x-(-6)), so h = -6. The plus sign makes h negative.

Q: Can I check my answer by graphing?

Absolutely! The vertex should be the lowest point on the parabola since this opens upward. Plot a few points around x = 6 and you'll see they're all higher than y = 1.

Q: What does the vertex tell me about the parabola?

The vertex (6,1) tells you the parabola's minimum point is at x = 6 with a y-value of 1. It also tells you the axis of symmetry is the vertical line x = 6.

Vertex Form with Direct Identification

Find the vertex of the parabola

$y=(x-6)^2+1$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the vertex of the parabola

00:03 We'll use the formula to describe a parabolic function

00:09 The coordinates of the vertex are (P,K)

00:12 We'll use this formula and find the vertex point

00:17 We'll substitute appropriate values according to the given data

00:20 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Find the vertex of the parabola

$y=(x-6)^2+1$

Step-by-step solution

To find the vertex of the parabola given by the equation $y = (x-6)^2 + 1$ , we recognize that the equation is in vertex form $y = (x-h)^2 + k$ , where $(h, k)$ represents the vertex.

Step 1: Recognize that the standard vertex form of a parabola is $y = (x-h)^2 + k$ .
Step 2: Identify $h$ and $k$ directly from the equation.
Step 3: Compare the given equation $y = (x-6)^2 + 1$ to the standard form to determine the values of $h$ and $k$ .

From the equation $y = (x-6)^2 + 1$ , we identify:

$h = 6$ (the value that follows the minus sign in $(x-6)$ )
$k = 1$ (the constant term added outside the squared term)

The vertex of the parabola is therefore $(h, k) = (6, 1)$ .

Thus, the vertex of the parabola is $(6, 1)$ .

Final Answer

$(6,1)$

Key Points to Remember

Essential concepts to master this topic

Vertex Form: Use $y = (x-h)^2 + k$ where vertex is (h,k)
Technique: From $y = (x-6)^2 + 1$ , h = 6 and k = 1
Check: Substitute x = 6: $y = (6-6)^2 + 1 = 1$ gives point (6,1) ✓

Common Mistakes

Avoid these frequent errors

Confusing the sign of h in vertex form
Don't read (x-6) and think h = -6! The vertex form is (x-h), so when you see (x-6), you need h = +6. Always remember: if it's (x-6), then h = 6; if it's (x+6), then h = -6.

Practice Quiz

Test your knowledge with interactive questions

Find the standard representation of the following function:

$$ f(x)=(x-3)^2+x $$

FAQ

Everything you need to know about this question

Why is the vertex (6,1) and not (-6,1)?

This is the most common mistake! In vertex form $y = (x-h)^2 + k$ , when you see (x-6), the h-value is positive 6, not negative 6. Think of it as x minus 6 equals zero when x = 6.

How do I remember which number is h and which is k?

Easy trick: h is the number inside the parentheses (affects x-coordinate), and k is the number outside the parentheses (affects y-coordinate). So in $(x-6)^2 + 1$ , h = 6 and k = 1.

What if the equation was y = (x+6)² + 1 instead?

Then the vertex would be (-6, 1)! When you see (x+6), that's the same as (x-(-6)), so h = -6. The plus sign makes h negative.

Can I check my answer by graphing?

Absolutely! The vertex should be the lowest point on the parabola since this opens upward. Plot a few points around x = 6 and you'll see they're all higher than y = 1.

What does the vertex tell me about the parabola?

The vertex (6,1) tells you the parabola's minimum point is at x = 6 with a y-value of 1. It also tells you the axis of symmetry is the vertical line x = 6.

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Locate the Vertex of the Parabola: y = (x-6)² + 1

Vertex Form with Direct Identification

❤️ 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 (6,1) and not (-6,1)?

How do I remember which number is h and which is k?

What if the equation was y = (x+6)² + 1 instead?

Can I check my answer by graphing?

What does the vertex tell me about the parabola?

🌟 Unlock Your Math Potential

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