Pinpointing the Vertex: Analyzing the Quadratic Equation y = (x+1)² - 1

Q: Why is the x-coordinate -1 when I see +1 in the equation?

Great question! The vertex form is $ y = a(x-h)^2 + k $. When you see $ (x+1)^2 $, rewrite it as $ (x-(-1))^2 $. So h = -1, making the vertex x-coordinate -1.

Q: How do I remember which coordinate is which?

Use the pattern (h, k) where h comes from inside the parentheses and k is the number added/subtracted outside. In $ y = (x+1)^2 - 1 $, h = -1 and k = -1, so vertex is (-1, -1).

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

You'd need to complete the square to convert it! But this equation $ y = (x+1)^2 - 1 $ is already in perfect vertex form, so you can read the vertex directly.

Q: Can I check my answer by graphing?

Absolutely! The vertex is the lowest point (for upward parabolas) or highest point (for downward parabolas). Plot (-1, -1) and verify it's the turning point of your parabola.

Q: Why does this parabola open upward?

Because the coefficient of the squared term is positive 1. In $ y = (x+1)^2 - 1 $, there's an invisible +1 in front, so the parabola opens upward with vertex as the minimum point.

Vertex Form with Standard Transformations

Find the vertex of the parabola

$y=(x+1)^2-1$

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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

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

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

00:25 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

$y=(x+1)^2-1$

Step-by-step solution

The given equation of the parabola is $y = (x+1)^2 - 1$ .

This equation is already in the vertex form, $y = a(x-h)^2 + k$ , where $(h, k)$ is the vertex.

By comparing, we identify:
The expression $(x + 1)$ implies that $h = -1$ (since $x + 1$ is equivalent to $(x - (-1))$ ).
The constant $-1$ is the $k$ value.

Thus, the vertex $(h, k)$ is $(-1, -1)$ .

Therefore, the vertex of the parabola is at the point $(-1,-1)$ .

Final Answer

$(-1,-1)$

Key Points to Remember

Essential concepts to master this topic

Vertex Form: y = a(x-h)² + k gives vertex at (h,k)
Sign Rule: (x+1)² means h = -1, opposite of inner sign
Verify: Check (-1,-1): y = (-1+1)² - 1 = 0 - 1 = -1 ✓

Common Mistakes

Avoid these frequent errors

Using the wrong sign for the h-coordinate
Don't read (x+1)² as h = +1! The +1 inside means you move LEFT to x = -1, not right. This gives wrong vertex coordinates completely. Always remember: (x-h)² form means the opposite sign for h-value.

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 x-coordinate -1 when I see +1 in the equation?

Great question! The vertex form is $y = a(x-h)^2 + k$ . When you see $(x+1)^2$ , rewrite it as $(x-(-1))^2$ . So h = -1, making the vertex x-coordinate -1.

How do I remember which coordinate is which?

Use the pattern (h, k) where h comes from inside the parentheses and k is the number added/subtracted outside. In $y = (x+1)^2 - 1$ , h = -1 and k = -1, so vertex is (-1, -1).

What if the equation isn't in vertex form?

You'd need to complete the square to convert it! But this equation $y = (x+1)^2 - 1$ is already in perfect vertex form, so you can read the vertex directly.

Can I check my answer by graphing?

Absolutely! The vertex is the lowest point (for upward parabolas) or highest point (for downward parabolas). Plot (-1, -1) and verify it's the turning point of your parabola.

Why does this parabola open upward?

Because the coefficient of the squared term is positive 1. In $y = (x+1)^2 - 1$ , there's an invisible +1 in front, so the parabola opens upward with vertex as the minimum point.

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Pinpointing the Vertex: Analyzing the Quadratic Equation y = (x+1)² - 1

Vertex Form with Standard Transformations

❤️ 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 x-coordinate -1 when I see +1 in the equation?

How do I remember which coordinate is which?

What if the equation isn't in vertex form?

Can I check my answer by graphing?

Why does this parabola open upward?

🌟 Unlock Your Math Potential

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