Find the Vertex: Analyzing y = (x-3)² - 10

Q: Why is h = 3 when I see (x - 3)?

This trips up many students! In vertex form $ y = a(x-h)^2 + k $, we have (x - h). So when you see $ (x-3) $, that means h = 3, not h = -3.

Q: How do I remember which number is x and which is y in the vertex?

The vertex is always written as (x-coordinate, y-coordinate) or (h, k). The h value comes from inside the parentheses, and k is the number added or subtracted at the end.

Q: What if the equation was y = (x + 3)² - 10?

Great question! $ (x+3)^2 $ is the same as $ (x-(-3))^2 $, so h = -3. The vertex would be (-3, -10) instead.

Q: Can I check my answer by plugging in the vertex?

Absolutely! Substitute your vertex coordinates into the original equation. The vertex is where the parabola reaches its minimum or maximum, so $ x = 3 $ should give you $ y = -10 $.

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

The vertex $ (3, -10) $ tells you the parabola's turning point. Since a = 1 (positive), this parabola opens upward and has its minimum value of -10 when x = 3.

Vertex Form with Direct Identification

Find the vertex of the parabola

$y=(x-3)^2-10$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the vertex coordinates of the parabola

00:03 Use the formula to describe the parabola function

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

00:13 Use this formula and find the vertex coordinates

00:18 Substitute appropriate values according to the given data

00:22 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

$y=(x-3)^2-10$

Step-by-step solution

To solve this problem, we'll find the vertex of the parabola given by the function $y = (x-3)^2 - 10$ .

Step 1: Recognize the function's form. The equation is written in the vertex form of a quadratic function: $y = a(x-h)^2 + k$ .
Step 2: Identify the values of $h$ and $k$ from the function. Here, $(x-3)^2$ indicates that $h = 3$ and the $-10$ outside the square indicates $k = -10$ .

By substituting into the vertex form, we see that the vertex of the parabola is $(h, k) = (3, -10)$ .

Therefore, the vertex of the parabola is $(3, -10)$ .

Final Answer

$(3,-10)$

Key Points to Remember

Essential concepts to master this topic

Vertex Form: Standard form is $y = a(x-h)^2 + k$ where vertex is (h,k)
Technique: From $(x-3)^2 - 10$ , h = 3 and k = -10
Check: Substitute vertex into equation: $y = (3-3)^2 - 10 = -10$ ✓

Common Mistakes

Avoid these frequent errors

Confusing signs when identifying h and k values
Don't read $(x-3)^2$ as h = -3! The negative inside the parentheses means h = +3. Always remember that $(x-h)^2$ gives you the opposite sign for h.

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 h = 3 when I see (x - 3)?

This trips up many students! In vertex form $y = a(x-h)^2 + k$ , we have (x - h). So when you see $(x-3)$ , that means h = 3, not h = -3.

How do I remember which number is x and which is y in the vertex?

The vertex is always written as (x-coordinate, y-coordinate) or (h, k). The h value comes from inside the parentheses, and k is the number added or subtracted at the end.

What if the equation was y = (x + 3)² - 10?

Great question! $(x+3)^2$ is the same as $(x-(-3))^2$ , so h = -3. The vertex would be (-3, -10) instead.

Can I check my answer by plugging in the vertex?

Absolutely! Substitute your vertex coordinates into the original equation. The vertex is where the parabola reaches its minimum or maximum, so $x = 3$ should give you $y = -10$ .

What does the vertex tell me about the parabola?

The vertex $(3, -10)$ tells you the parabola's turning point. Since a = 1 (positive), this parabola opens upward and has its minimum value of -10 when x = 3.

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Find the Vertex: Analyzing y = (x-3)² - 10

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 h = 3 when I see (x - 3)?

How do I remember which number is x and which is y in the vertex?

What if the equation was y = (x + 3)² - 10?

Can I check my answer by plugging in the vertex?

What does the vertex tell me about the parabola?

🌟 Unlock Your Math Potential

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