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

Q: Why does (x+2)² mean h = -2 and not h = +2?

The vertex form is $ y = a(x-h)^2 + k $ with a minus sign before h. So $ (x+2)^2 $ must be rewritten as $ (x-(-2))^2 $ to match the pattern, giving us $ h = -2 $.

Q: How do I remember which coordinate is which in the vertex?

Think of it as (h, k) where h comes from the x-part inside parentheses and k is the number added/subtracted at the end. In $ (x+2)^2 - 3 $, h = -2 (x-coordinate) and k = -3 (y-coordinate).

Q: What if there's no number in front of the squared term?

When there's no visible coefficient, it means $ a = 1 $. This doesn't change the vertex location at all - you still find h and k the same way. The coefficient a only affects whether the parabola opens up or down and how wide it is.

Q: Can I just plug in x = -2 to find the y-coordinate?

Absolutely! That's actually a great way to double-check. When $ x = -2 $: $ y = (-2+2)^2 - 3 = 0^2 - 3 = -3 $. This confirms the vertex is $ (-2, -3) $.

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

If you have something like $ y = x^2 + 4x + 1 $, you'll need to complete the square first to get it into vertex form. But in this problem, $ y = (x+2)^2 - 3 $ is already in perfect vertex form!

Vertex Form with Sign Recognition

Find the vertex of the parabola

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's find the vertex of the parabola.

00:09 We'll use a formula to describe the parabolic function.

00:16 The vertex coordinates are given as P and K.

00:20 Using this formula, we'll locate the vertex point. Ready?

00:26 Notice that in the formula, the value of P is negative.

00:34 We'll substitute the right values based on the data we have.

00:38 And there you go! That's how we solve 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

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

Step-by-step solution

To find the vertex of the parabola given by the equation $y = (x+2)^2 - 3$ , we will use our understanding of the vertex form of a quadratic equation.

The vertex form of a quadratic equation is expressed as:

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

In this formula, the vertex of the parabola is located at the point $(h, k)$ .

Now, let's compare the given equation $y = (x+2)^2 - 3$ with the standard vertex form:

Notice that the expression inside the bracket is $(x+2)$ . This can be rewritten as $(x - (-2))$ , which highlights that $h = -2$ .
The constant term at the end is $-3$ , which corresponds to $k = -3$ .

Therefore, the vertex of the parabola is $(-2, -3)$ .

Checking against the provided choices, the correct answer is option 1: $(-2, -3)$ .

Thus, we conclude that the vertex of the parabola is $(-2, -3)$ .

Final Answer

$(-2,-3)$

Key Points to Remember

Essential concepts to master this topic

Vertex Form: $y = a(x-h)^2 + k$ gives vertex at $(h,k)$
Sign Recognition: $(x+2)^2$ means $(x-(-2))^2$ , so $h = -2$
Verification: Check that vertex $(-2,-3)$ satisfies: $(-2+2)^2-3 = -3$ ✓

Common Mistakes

Avoid these frequent errors

Confusing signs when identifying h-value
Don't think (x+2)² means h = +2! This gives vertex (2,-3) instead of (-2,-3). The plus sign inside the parentheses actually means h is negative. Always rewrite (x+2) as (x-(-2)) to see that h = -2.

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 does (x+2)² mean h = -2 and not h = +2?

The vertex form is $y = a(x-h)^2 + k$ with a minus sign before h. So $(x+2)^2$ must be rewritten as $(x-(-2))^2$ to match the pattern, giving us $h = -2$ .

How do I remember which coordinate is which in the vertex?

Think of it as (h, k) where h comes from the x-part inside parentheses and k is the number added/subtracted at the end. In $(x+2)^2 - 3$ , h = -2 (x-coordinate) and k = -3 (y-coordinate).

What if there's no number in front of the squared term?

When there's no visible coefficient, it means $a = 1$ . This doesn't change the vertex location at all - you still find h and k the same way. The coefficient a only affects whether the parabola opens up or down and how wide it is.

Can I just plug in x = -2 to find the y-coordinate?

Absolutely! That's actually a great way to double-check. When $x = -2$ : $y = (-2+2)^2 - 3 = 0^2 - 3 = -3$ . This confirms the vertex is $(-2, -3)$ .

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

If you have something like $y = x^2 + 4x + 1$ , you'll need to complete the square first to get it into vertex form. But in this problem, $y = (x+2)^2 - 3$ is already in perfect vertex form!

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

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 does (x+2)² mean h = -2 and not h = +2?

How do I remember which coordinate is which in the vertex?

What if there's no number in front of the squared term?

Can I just plug in x = -2 to find the y-coordinate?

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

🌟 Unlock Your Math Potential

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