Find the Vertex of y=(x+2)²-2: Quadratic Function Analysis

Q: Why is the x-coordinate negative when I see +2 in the equation?

The vertex form is $ y = a(x-h)^2 + k $ with a minus sign before h. When you see $ (x+2)^2 $, think of it as $ (x-(-2))^2 $, so h = -2.

Q: How do I remember which coordinate is which?

Use the memory trick: h comes before k in the alphabet, and x comes before y in coordinates. So vertex = (h, k) = (x-coordinate, y-coordinate).

Q: What if the equation doesn't look like vertex form?

If you see $ y = ax^2 + bx + c $, you need to complete the square first to convert it to vertex form. But this equation is already in vertex form!

Q: Does the 'a' value 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 (h, k) stays the same regardless of 'a'.

Vertex Form with Sign Identification

Find the vertex of the parabola

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

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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 the parabola function

00:08 The coordinates of the vertex are (P,K)

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

00:16 We notice that according to the formula, the term P is negative

00:27 We'll substitute appropriate values according to the given data

00:30 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

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

Step-by-step solution

To solve the problem of finding the vertex of the parabola represented by $y = (x+2)^2 - 2$ , consider the form of the equation.

This equation is written in the vertex form of a quadratic function, which is given by:

$y = a(x-h)^2 + k$

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

Comparing $y = (x+2)^2 - 2$ with the standard form $y = a(x-h)^2 + k$ , we identify:

$h = -2$ because the expression is $(x - (-2))^2$
$k = -2$

Therefore, the vertex of the parabola is $(-2, -2)$ .

The correct answer is $(-2, -2)$ .

Final Answer

$(-2,-2)$

Key Points to Remember

Essential concepts to master this topic

Vertex Form: In $y = a(x-h)^2 + k$ , vertex is always $(h, k)$
Sign Rule: For $(x+2)^2$ , rewrite as $(x-(-2))^2$ so h = -2
Verify: Substitute x = -2: $y = (-2+2)^2 - 2 = 0 - 2 = -2$ ✓

Common Mistakes

Avoid these frequent errors

Misidentifying the h-value from (x+2)²
Don't think h = +2 just because you see +2 in the parentheses = wrong vertex (2,-2)! The vertex form is (x-h)², so (x+2)² means (x-(-2))², making h = -2. Always rewrite (x+number)² as (x-(-number))² to find h correctly.

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 x-coordinate negative when I see +2 in the equation?

The vertex form is $y = a(x-h)^2 + k$ with a minus sign before h. When you see $(x+2)^2$ , think of it as $(x-(-2))^2$ , so h = -2.

How do I remember which coordinate is which?

Use the memory trick: h comes before k in the alphabet, and x comes before y in coordinates. So vertex = (h, k) = (x-coordinate, y-coordinate).

What if the equation doesn't look like vertex form?

If you see $y = ax^2 + bx + c$ , you need to complete the square first to convert it to vertex form. But this equation is already in vertex form!

Can I check my vertex answer somehow?

Yes! Substitute the x-coordinate back into the equation. You should get the y-coordinate. For (-2, -2): $y = (-2+2)^2 - 2 = 0 - 2 = -2$ ✓

Does the 'a' value 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 (h, k) stays the same regardless of 'a'.

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Find the Vertex of y=(x+2)²-2: Quadratic Function Analysis

Vertex Form with Sign 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 x-coordinate negative when I see +2 in the equation?

How do I remember which coordinate is which?

What if the equation doesn't look like vertex form?

Can I check my vertex answer somehow?

Does the 'a' value affect the vertex location?

🌟 Unlock Your Math Potential

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