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

Q: Why is the vertex (-3, -6) and not (3, -6)?

This trips up many students! In vertex form $ y = a(x-h)^2 + k $, we have negative h inside the parentheses. Since our equation is $ (x+3)^2 $, we can rewrite it as $ (x-(-3))^2 $, so $ h = -3 $.

Q: How do I remember which coordinate is which?

Use the pattern "h, k" = "x, y". The value of h (which comes from the x-term) is the x-coordinate, and k (the constant term) is the y-coordinate of the vertex.

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

If you see something like $ y = x^2 + 6x + 3 $, you'll need to complete the square first to get it into $ y = (x-h)^2 + k $ form before finding the vertex.

Q: Can I just plug in x = -3 to check my answer?

Absolutely! When $ x = -3 $: $ y = (-3+3)^2 - 6 = 0^2 - 6 = -6 $. This confirms our vertex is $ (-3, -6) $.

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 location depends only on the values of h and k.

Vertex Form with Direct Identification

Find the vertex of the parabola

$y=(x+3)^2-6$

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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

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

00:13 We'll use this formula to find the vertex point

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

00:26 We'll substitute appropriate values according to the given data

00:31 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

$y=(x+3)^2-6$

Step-by-step solution

To solve this problem, we'll utilize the properties of the vertex form.

Step 1: Identify the form of the quadratic equation. It is given as $y = (x+3)^2 - 6$ .
Step 2: Recognize this as a vertex form equation $y = a(x-h)^2 + k$ .
Step 3: Compare to identify $h$ and $k$ . Here, $h = -3$ and $k = -6$ .
Step 4: Determine the vertex of the parabola, which is $(-3, -6)$ .

In the vertex form, $a(x-h)^2 + k$ , the vertex is simply $(h, k)$ . For the equation $y = (x+3)^2 - 6$ , $h$ is $-3$ and $k$ is $-6$ .
Thus, the vertex of the parabola is $(-3, -6)$ .

Therefore, the solution to the problem is $(-3, -6)$ .

Final Answer

$(-3,-6)$

Key Points to Remember

Essential concepts to master this topic

Vertex Form: $y = a(x-h)^2 + k$ has vertex at $(h,k)$
Sign Rule: $(x+3)^2$ means $h = -3$ , not positive 3
Verification: Substitute $x = -3$ : $y = (-3+3)^2 - 6 = 0 - 6 = -6$ ✓

Common Mistakes

Avoid these frequent errors

Confusing the sign of h in vertex form
Don't read $(x+3)^2$ as $h = +3$ = vertex at $(3,-6)$ ! The standard form is $(x-h)^2$ , so $(x+3)^2 = (x-(-3))^2$ means $h = -3$ . Always rewrite as $(x-h)$ form to identify the correct sign.

Practice Quiz

Test your knowledge with interactive questions

The following function has been plotted on the graph below:

$$ f(x)=x^2-8x+16 $$

Calculate point C.

FAQ

Everything you need to know about this question

Why is the vertex (-3, -6) and not (3, -6)?

This trips up many students! In vertex form $y = a(x-h)^2 + k$ , we have negative h inside the parentheses. Since our equation is $(x+3)^2$ , we can rewrite it as $(x-(-3))^2$ , so $h = -3$ .

How do I remember which coordinate is which?

Use the pattern "h, k" = "x, y". The value of h (which comes from the x-term) is the x-coordinate, and k (the constant term) is the y-coordinate of the vertex.

What if the equation isn't in perfect vertex form?

If you see something like $y = x^2 + 6x + 3$ , you'll need to complete the square first to get it into $y = (x-h)^2 + k$ form before finding the vertex.

Can I just plug in x = -3 to check my answer?

Absolutely! When $x = -3$ : $y = (-3+3)^2 - 6 = 0^2 - 6 = -6$ . This confirms our vertex is $(-3, -6)$ .

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 location depends only on the values of h and k.

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

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 (-3, -6) and not (3, -6)?

How do I remember which coordinate is which?

What if the equation isn't in perfect vertex form?

Can I just plug in x = -3 to check my answer?

Does the 'a' value affect the vertex location?

🌟 Unlock Your Math Potential

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