Locate the Vertex of the Parabola: y = (x + 7)² + 15

Q: Why does (x+7) mean h = -7 and not h = 7?

The vertex form is $ y = (x-h)^2 + k $, so you need x minus h. To get (x+7), you need x - (-7), which means h = -7.

Q: How can I remember the sign change rule?

Think of it as "opposite day" - whatever sign you see inside the parentheses, the h-coordinate has the opposite sign. Plus becomes minus, minus becomes plus!

Q: What if the equation was y = (x-3)² + 8?

Then h = 3 (positive 3) and k = 8, so the vertex is (3, 8). Remember: (x-3) means h = 3, while (x+3) means h = -3.

Vertex Form with Sign Recognition

Find the vertex of the parabola

$y=(x+7)^2+15$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

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

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

00:18 We can see that according to the formula P is negative

00:23 We'll use this formula to find the vertex point

00:29 We'll substitute appropriate values according to the given data

00:35 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

$y=(x+7)^2+15$

Step-by-step solution

To solve the problem, we follow these steps:

Step 1: Recognize the form of the equation. The equation is given as $y = (x+7)^2 + 15$ , which is in vertex form.
Step 2: Identify the vertex from the equation. The vertex form of a parabola is $y = (x-h)^2 + k$ , where the vertex is $(h, k)$ .
Step 3: Determine the values of $h$ and $k$ . Here, $(x+7)$ means that $h = -7$ (notice the sign change), and the constant $+15$ is $k = 15$ .

By recognizing the form of the equation and substituting the values, the vertex of the parabola is $(-7, 15)$ .

Final Answer

$(-7,15)$

Key Points to Remember

Essential concepts to master this topic

Vertex Form: $y = (x-h)^2 + k$ has vertex at $(h, k)$
Sign Change: $(x+7)^2$ means h = -7, not +7
Check: Substitute x = -7: $y = (-7+7)^2 + 15 = 0 + 15 = 15$ ✓

Common Mistakes

Avoid these frequent errors

Using wrong sign for h-coordinate
Don't read (x+7) as h = 7! This gives vertex (7,15) instead of (-7,15). The vertex form y = (x-h)² + k requires you to flip the sign inside parentheses. Always remember: (x+7) means h = -7 because x - (-7) = x + 7.

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 does (x+7) mean h = -7 and not h = 7?

The vertex form is $y = (x-h)^2 + k$ , so you need x minus h. To get (x+7), you need x - (-7), which means h = -7.

How can I remember the sign change rule?

Think of it as "opposite day" - whatever sign you see inside the parentheses, the h-coordinate has the opposite sign. Plus becomes minus, minus becomes plus!

What if the equation was y = (x-3)² + 8?

Then h = 3 (positive 3) and k = 8, so the vertex is (3, 8). Remember: (x-3) means h = 3, while (x+3) means h = -3.

How do I verify my vertex is correct?

Substitute the x-coordinate back into the equation. At x = -7: $y = (-7+7)^2 + 15 = 0^2 + 15 = 15$ . This gives the point (-7, 15)!

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

Yes! If there's no coefficient in front of the squared term (or it's positive), the parabola opens upward. A negative coefficient would make it open downward.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 The Quadratic Function questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

Locate the Vertex of the Parabola: y = (x + 7)² + 15

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+7) mean h = -7 and not h = 7?

How can I remember the sign change rule?

What if the equation was y = (x-3)² + 8?

How do I verify my vertex is correct?

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

🌟 Unlock Your Math Potential

More Questions

The Vertex of the Parabola

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

Determine the Vertex of the Parabola: y = (x-3)² - 1

Discover the Vertex of the Parabola: Analyzing y = (x-7) - 7

Calculate the Vertex of y = (x-3)² + 6

Vertex Representation

Locate the Vertex: Solving y = (x-7) + 5 for the Quadratic Peak

Find the Vertex of the Parabola: (x-1)²-1

Identify the Vertex in the Equation y=(x+1)²: A Quadratic Guide

Transforming the Function: Reveal the Standard Form of f(x) = (x+5)² + 3