Uncover the Vertex: Parabola Described by y=(x+8)²-9

Q: Why is the vertex (-8,-9) and not (8,-9)?

The vertex form is $ y = (x-h)^2 + k $. Since we have $ (x+8)^2 $, we can rewrite this as $ (x-(-8))^2 $. So h = -8, not +8!

Q: How do I remember which sign to use for h?

Use the opposite sign! If you see (x + number), then h is negative. If you see (x - number), then h is positive. The k value keeps its original sign.

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

You would need to complete the square first to convert it to vertex form $ y = (x-h)^2 + k $. But this problem is already in the right form!

Q: Does the vertex tell me if the parabola opens up or down?

Not directly from the vertex coordinates! Look at the coefficient of the squared term. Since we have $ (x+8)^2 $ (positive 1), the parabola opens upward.

Vertex Form with Sign Recognition

Find the vertex of the parabola

$y=(x+8)^2-9$

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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

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

00:20 We'll use this formula and find the vertex point

00:29 We notice that according to the formula P is negative

00:36 We'll substitute appropriate values according to the given data

00:41 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

$y=(x+8)^2-9$

Step-by-step solution

To solve for the vertex of the parabola, we need to recognize that the equation $y = (x+8)^2 - 9$ is already in vertex form, which is $y = (x-h)^2 + k$ .

Let's break down the given equation:

Rewrite the given equation: $y = (x+8)^2 - 9$ .
This matches the vertex form $y = (x - h)^2 + k$ .
Identify values: Here, $h = -8$ and $k = -9$ .

Thus, the vertex is located at the point $(-8, -9)$ .

Comparing with the multiple-choice options provided:

Choice 1: $(-8, 9)$ - Incorrect $k$ .
Choice 2: $(8, -9)$ - Incorrect $h$ .
Choice 3: $(8, 9)$ - Incorrect both $h$ and $k$ .
Choice 4: $(-8, -9)$ - Correct.

Therefore, the vertex of the parabola is $(-8, -9)$ .

Final Answer

$(-8,-9)$

Key Points to Remember

Essential concepts to master this topic

Vertex Form: For $y = (x-h)^2 + k$ , vertex is (h, k)
Sign Rule: $(x+8)^2$ means h = -8, not +8
Check: Substitute vertex coordinates: $y = (-8+8)^2 - 9 = -9$ ✓

Common Mistakes

Avoid these frequent errors

Confusing signs when identifying h and k values
Don't read (x+8) as h = +8 = wrong vertex (8,-9)! The vertex form is (x-h), so (x+8) = (x-(-8)), meaning h = -8. Always remember: opposite sign for h, same sign for k.

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 (-8,-9) and not (8,-9)?

The vertex form is $y = (x-h)^2 + k$ . Since we have $(x+8)^2$ , we can rewrite this as $(x-(-8))^2$ . So h = -8, not +8!

How do I remember which sign to use for h?

Use the opposite sign! If you see (x + number), then h is negative. If you see (x - number), then h is positive. The k value keeps its original sign.

What if the equation isn't in vertex form?

You would need to complete the square first to convert it to vertex form $y = (x-h)^2 + k$ . But this problem is already in the right form!

How can I check if my vertex is correct?

Substitute the x-coordinate of your vertex back into the equation. The y-value you get should match the y-coordinate of your vertex. For (-8,-9): $y = (-8+8)^2 - 9 = 0 - 9 = -9$ ✓

Does the vertex tell me if the parabola opens up or down?

Not directly from the vertex coordinates! Look at the coefficient of the squared term. Since we have $(x+8)^2$ (positive 1), the parabola opens upward.

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Uncover the Vertex: Parabola Described by y=(x+8)²-9

Vertex Form with Sign Recognition

❤️ 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 (-8,-9) and not (8,-9)?

How do I remember which sign to use for h?

What if the equation isn't in vertex form?

How can I check if my vertex is correct?

Does the vertex tell me if the parabola opens up or down?

🌟 Unlock Your Math Potential

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