thank you ### Intersection of Blue and Yellow Birds' Paths**Problem Statement:** Where did the blue and yellow birds’ paths crash into one another? There are two actual points of intersection. Solve this problem algebraically.#### Equations of Paths- **Blue equation:** $ y = -1(x - 10) + 36 $- **Yellow equation:** $ y = -\frac{9}{40}(x - 13)^2 + 38.025 $To find the points of intersection, set the equations equal to each other and solve for $ x $:\[ -1(x - 10) + 36 = -\frac{9}{40}(x - 13)^2 + 38.025 \]Simplify and solve the equation for $ x $. Once you have the values of $ x $, substitute them back into either the blue or yellow equation to find the corresponding $ y $ coordinates. This algebraic solution will provide the two points of intersection where the paths of the blue and yellow birds crash into one another. **Graph Analysis using Desmos:**In this Desmos plot, we observe two quadratic functions displayed on the graph. The purpose of this illustration is to compare the differences between the two parabolic curves represented by the given equations.1. **Equations:** - The first function is $ y = -1(x - 10)^2 + 36 $. - The second function is $ y = -\frac{9}{40}(x - 13)^2 + 38.025 $.2. **Graph Details:** - The x-axis ranges from approximately 0 to 20. - The y-axis ranges from 20 to 40. - Both parabolas open downwards, indicating the presence of a negative coefficient for the quadratic term in both equations.3. **Explanation of the functions:** - For the first function $ y = -1(x - 10)^2 + 36 $: - The vertex of the parabola is at (10, 36). - The parabola opens downward with a leading coefficient of -1, indicating it is relatively narrow. - For the second function $ y = -\frac{9}{40}(x - 13)^2 + 38.025 $: - The vertex of the parabola is at (13, 38.025). - The parabola opens downward with a leading coefficient of $-\frac{9}{40}$, making this parabola wider in comparison to the first one.4. **Graphical Appearance:** - The first parabola (in blue) peaks at a lower point and is steeper compared to the second parabola. - The second parabola (in green) peaks at a higher point and is broader, demonstrating its wider spread on the graph.The graph visually demonstrates how changes in the quadratic and linear coefficients, as well as the vertex form, affect the shape and positioning of the parabolas on a coordinate plane. This comparison is essential for understanding the properties and behaviors of quadratic functions in algebra.

Name: thank you ### Intersection of Blue and Yellow Birds' Paths**Problem St
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Description: thank you ### Intersection of Blue and Yellow Birds' Paths**Problem Statement:** Where did the blue and yellow birds’ paths crash into one another? There are two actual points of intersection. Solve this problem algebraically.#### Equations of Paths-

The given equations are: We have to solve the equations.

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Algebra

Where did the blue and yellow birds' paths crash into one another? There are two actual points of intersection. Solve this problem algebraically. Blue equation : y=-1(x-10)+36 Yellow equation: y= y= -9/40(x – 13)* + 38.025

Where did the blue and yellow birds' paths crash into one another? There are two actual points of intersection. Solve this problem algebraically. Blue equation : y=-1(x-10)+36 Yellow equation: y= y= -9/40(x – 13)* + 38.025

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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thank you

### Intersection of Blue and Yellow Birds' Paths

**Problem Statement:**
Where did the blue and yellow birds’ paths crash into one another? There are two actual points of intersection. Solve this problem algebraically.

#### Equations of Paths
- **Blue equation:** $ y = -1(x - 10) + 36 $
- **Yellow equation:** $ y = -\frac{9}{40}(x - 13)^2 + 38.025 $

To find the points of intersection, set the equations equal to each other and solve for $ x $:

\[ -1(x - 10) + 36 = -\frac{9}{40}(x - 13)^2 + 38.025 \]

Simplify and solve the equation for $ x $. Once you have the values of $ x $, substitute them back into either the blue or yellow equation to find the corresponding $ y $ coordinates.

This algebraic solution will provide the two points of intersection where the paths of the blue and yellow birds crash into one another.

**Graph Analysis using Desmos:**

In this Desmos plot, we observe two quadratic functions displayed on the graph. The purpose of this illustration is to compare the differences between the two parabolic curves represented by the given equations.

1. **Equations:**
- The first function is $ y = -1(x - 10)^2 + 36 $.
- The second function is $ y = -\frac{9}{40}(x - 13)^2 + 38.025 $.

2. **Graph Details:**
- The x-axis ranges from approximately 0 to 20.
- The y-axis ranges from 20 to 40.
- Both parabolas open downwards, indicating the presence of a negative coefficient for the quadratic term in both equations.

3. **Explanation of the functions:**
- For the first function $ y = -1(x - 10)^2 + 36 $:
- The vertex of the parabola is at (10, 36).
- The parabola opens downward with a leading coefficient of -1, indicating it is relatively narrow.

- For the second function $ y = -\frac{9}{40}(x - 13)^2 + 38.025 $:
- The vertex of the parabola is at (13, 38.025).
- The parabola opens downward with a leading coefficient of $-\frac{9}{40}$, making this parabola wider in comparison to the first one.

4. **Graphical Appearance:**
- The first parabola (in blue) peaks at a lower point and is steeper compared to the second parabola.
- The second parabola (in green) peaks at a higher point and is broader, demonstrating its wider spread on the graph.

The graph visually demonstrates how changes in the quadratic and linear coefficients, as well as the vertex form, affect the shape and positioning of the parabolas on a coordinate plane. This comparison is essential for understanding the properties and behaviors of quadratic functions in algebra.

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