Solve for Y-Coordinates of Intersection | Simple Problem with f(y) and g(y)

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In summary, solving for the y-coordinates of intersection is a process used to find the points where two functions intersect on a graph. This can provide important information about the relationship between the functions and can be used to solve equations or analyze real-world situations. This is done by setting the two functions equal to each other and solving for y, using algebraic methods or a graphing calculator. If there are multiple points of intersection, all of the y-coordinates must be found. This process has many real-world applications, from business and manufacturing to scientific studies and engineering.
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BuBbLeS01
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Simple problem...need help PlEaSe!

Homework Statement


Okay so I am trying to find the area of a region but I having a problem with a simple intermediate step! I have...
f(y) = y^2
g(y) = y + 2
I need to find the y-coordinates of where the 2 lines intersect. Can someone please help me?


Homework Equations





The Attempt at a Solution

 
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  • #2
Set them equal to each other and solve for y.
 
  • #3
At the point of intersection, y2= y+ 2. Solve y2- y- 2= 0.
 

FAQ: Solve for Y-Coordinates of Intersection | Simple Problem with f(y) and g(y)

What is the purpose of solving for the y-coordinates of intersection?

The purpose of solving for the y-coordinates of intersection is to determine the point(s) where two functions, f(y) and g(y), intersect on a graph. This can provide valuable information about the relationship between the two functions and can be used to find solutions to equations or to analyze real-world situations.

How do you solve for the y-coordinates of intersection?

To solve for the y-coordinates of intersection, you must set the two functions, f(y) and g(y), equal to each other and then solve for y. This can be done by using algebraic methods such as substitution, elimination, or graphing. Once you have found the y-coordinates of intersection, you can then plug them back into either of the original functions to find the corresponding x-coordinates.

What if there are multiple points of intersection between the two functions?

If there are multiple points of intersection between the two functions, you will need to find all of the y-coordinates of intersection. This can be done by setting the two functions equal to each other and solving for y. You may need to use different algebraic methods for each set of equations. Once you have found all of the y-coordinates, you can then plug them back into either of the original functions to find the corresponding x-coordinates.

Can you use a graphing calculator to solve for the y-coordinates of intersection?

Yes, you can use a graphing calculator to solve for the y-coordinates of intersection. Many graphing calculators have a "intersect" function that allows you to find the points of intersection between two graphs. You can also use the "zero" or "root" function to find the x-intercepts, which can then be used to find the corresponding y-coordinates.

What are some real-world applications of solving for the y-coordinates of intersection?

Solving for the y-coordinates of intersection can be useful in many real-world situations, such as finding the break-even point in a business, determining the optimal production level in manufacturing, or analyzing the relationship between two variables in a scientific study. It can also be used to find solutions to equations and to understand the behavior of systems in physics and engineering.

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