https://file.aiquickdraw.com/mathbot/file/1727366271675avxki4lg.jpg

What is the equation of the blue graph?



 a
\large y=\left(x-1\right)^2+2

 b
\large y=\left(x+2\right)^2+1

 c
\large y=\left(x+2\right)^2-1

 d
\large y=\left(x-2\right)^2+1

 e
\large y=\left(x+1\right)^2-2

 f
\large y=\left(x-2\right)^2-1

 g
\large y=\left(x+1\right)^2+2

 h
\large y=\left(x-1\right)^2-2



The blue graph appears to be a downward or left-shifted parabola in the image. To determine the equation of the blue graph, let's analyze the transformation based on the standard form of a quadratic function, \( y = (x - h)^2 + k \), where:

- \( h \) represents the horizontal shift (left or right),
- \( k \) represents the vertical shift (up or down),
- The vertex of the parabola is located at \( (h, k) \).

From the image, the vertex of the blue parabola is at \( (-2, -1) \), meaning the graph is shifted 2 units to the left and 1 unit downward.

Thus, the equation for the blue parabola is:
\[
y = (x + 2)^2 - 1
\]

This corresponds to option **(c)**.

Would you like more details on how to transform equations of parabolas or discuss any other part of this topic?

Here are 5 related questions to explore:
1. How do horizontal and vertical shifts affect the equation of a parabola?
2. What is the vertex form of a quadratic equation and why is it useful?
3. How can you find the axis of symmetry from the equation of a parabola?
4. What are the effects of stretching or compressing a parabola on its graph?
5. How can you determine the direction in which a parabola opens?

**Tip:** When identifying the equation of a graph, always look for the vertex and direction first. The vertex helps you figure out the horizontal and vertical shifts.

Learn how to identify the equation of a quadratic function based on graph transformations. In this case, the blue graph represents a parabola with a vertex at (-2, -1), leading to the equation y = (x + 2)^2 - 1. Suitable for high school students learning about quadratic functions.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation