https://r2.erweima.ai/mathbot/image/1726273527259fly8nu1e.jpg

The equation given is in the form:

\[
y = (x - h)^2 + k
\]

This is the vertex form of a quadratic equation, where \((h, k)\) represents the vertex of the parabola.

In this case, comparing the given equation \( y = (x - 1)^2 + 1 \) with the general form, we can identify that:
- \( h = 1 \)
- \( k = 1 \)

So, the vertex is:

\[
\text{Vertex: } (1, 1)
\]

Would you like a detailed explanation on how to graph this, or do you have any other questions?

Here are 5 related questions:
1. How do you convert a quadratic equation from standard form to vertex form?
2. What is the significance of the vertex in a parabola's graph?
3. How does the value of \(h\) affect the position of the parabola along the x-axis?
4. How does the value of \(k\) affect the position of the parabola along the y-axis?
5. What are the effects of changing the coefficient of \((x - h)^2\) in a vertex form equation?

**Tip:** The vertex form is particularly useful for graphing parabolas, as it directly shows the vertex, making it easier to sketch or interpret the graph's key features.

Graph the following equation: y = (x - 1)^2 + 1. Identify the vertex.

Learn how to identify the vertex of the quadratic equation y = (x - 1)^2 + 1. This problem covers key algebraic concepts, including vertex form and its application in finding the vertex of a parabola. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation