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Finding the x-intersection of a function with the horizontal axis is a fundamental concept in mathematics and is of great importance in various applications. The x-intersection, also known as the x-intercept or roots, represents the points at which a function intersects the horizontal axis or the line y = 0. It is essential to determine these points as they provide valuable insights into the behavior and properties of the function. This guide will outline the step-by-step process to find the x-intersection of a function, equipping you with the necessary knowledge and techniques to solve such problems efficiently. Whether you are a student studying calculus or an individual working on real-world problems involving functions, understanding how to find the x-intersection can greatly enhance your problem-solving skills. So, let’s dive in and explore the various methods and strategies to find the x-intersection of a function with the horizontal axis.
This article was co-written by David Jia. David Jia is a tutoring teacher and founder of LA Math Tutoring, a private tutoring facility based in Los Angeles, California. With over 10 years of teaching experience, David teaches a wide variety of subjects to students of all ages and grades, as well as college admissions counseling and prep for SAT, ACT, ISEE, etc. scoring 800 in math and 690 in English on the SAT, David was awarded a Dickinson Scholarship to the University of Miami, where he graduated with a bachelor’s degree in business administration. Additionally, David has worked as an instructor in online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.
There are 7 references cited in this article that you can see at the bottom of the page.
This article has been viewed 123,628 times.
In algebra, a two-dimensional coordinate graph has a horizontal horizontal axis, also known as the x-axis, and a vertical vertical axis, also called the y-axis. Where lines representing a series of values intersect these axes is called intersection. The y-intersection of the function with the vertical axis is the point where the line intersects the y-axis, and the x-intersection of the function with the horizontal axis is where the line intersects the x-horizontal axis. For simple problems, it is easy to find the x-intersection of the function with the horizontal axis by looking at the graph. You can find the exact intersection by solving math problems using the equation of the line.
Steps
Using line graphs
![Image titled Find the X Intercept Step 1](https://www.wikihow.com/images_en/thumb/e/e7/Find-the-X-Intercept-Step-1-Version-3.jpg/v4-728px-Find-the-X-Intercept-Step-1-Version-3.jpg)
![Image titled Find the X Intercept Step 2](https://www.wikihow.com/images_en/thumb/7/7d/Find-the-X-Intercept-Step-2-Version-3.jpg/v4-728px-Find-the-X-Intercept-Step-2-Version-3.jpg)
![Image titled Find the X Intercept Step 3](https://www.wikihow.com/images_en/thumb/2/27/Find-the-X-Intercept-Step-3-Version-3.jpg/v4-728px-Find-the-X-Intercept-Step-3-Version-3.jpg)
- For example, if the line intersects the x-axis at point 4, the pair of values for the x-intersection of the function with the x-axis is (4,0){displaystyle(4,0)} .
Using the equation of the line
![Image titled Find the X Intercept Step 4](https://www.wikihow.com/images_en/thumb/c/c0/Find-the-X-Intercept-Step-4-Version-3.jpg/v4-728px-Find-the-X-Intercept-Step-4-Version-3.jpg)
- For example, you might have the equation 2x+3y=6{displaystyle 2x+3y=6} .
![Image titled Find the X Intercept Step 5](https://www.wikihow.com/images_en/thumb/e/e9/Find-the-X-Intercept-Step-5-Version-2.jpg/v4-728px-Find-the-X-Intercept-Step-5-Version-2.jpg)
- For example, if you substitute 0 for y{displaystyle y} , your equation will take the form: 2x+3(0)=6{displaystyle 2x+3(0)=6} , simplified would be 2x=6{displaystyle 2x=6} .
![Image titled Find the X Intercept Step 6](https://www.wikihow.com/images_en/thumb/6/66/Find-the-X-Intercept-Step-6-Version-2.jpg/v4-728px-Find-the-X-Intercept-Step-6-Version-2.jpg)
- For example:
2x=6{displaystyle 2x=6}
2x2=62{displaystyle {frac {2x}{2}}={frac {6}{2}}}
x=3{displaystyle x=3}
![Image titled Find the X Intercept Step 7](https://www.wikihow.com/images_en/thumb/b/b7/Find-the-X-Intercept-Step-7-Version-2.jpg/v4-728px-Find-the-X-Intercept-Step-7-Version-2.jpg)
- For example, for the line 2x+3y=6{displaystyle 2x+3y=6} , the intersection x will be at the point (3,0){displaystyle(3,0)} .
Using quadratic equation
![Image titled Find the X Intercept Step 8](https://www.wikihow.com/images_en/thumb/6/63/Find-the-X-Intercept-Step-8-Version-2.jpg/v4-728px-Find-the-X-Intercept-Step-8-Version-2.jpg)
- For example, the equation x2+3x−ten=0{displaystyle x^{2}+3x-10=0} is a quadratic equation, so this line will have two intersections with the horizontal axis.
![Image titled Find the X Intercept Step 9](https://www.wikihow.com/images_en/thumb/d/de/Find-the-X-Intercept-Step-9-Version-2.jpg/v4-728px-Find-the-X-Intercept-Step-9-Version-2.jpg)
![Image titled Find the X Intercept Step 10](https://www.wikihow.com/images_en/thumb/4/40/Find-the-X-Intercept-Step-10-Version-2.jpg/v4-728px-Find-the-X-Intercept-Step-10-Version-2.jpg)
- For example, if the equation of the line is x2+3x−ten=0{displaystyle x^{2}+3x-10=0} , your quadratic formula will take the form: x=−3±32−4(first)(−ten)2(first){displaystyle x={frac {-3pm {sqrt {3^{2}-4(1)(-10)}}}{2(1)}}} .
![Image titled Find the X Intercept Step 11](https://www.wikihow.com/images_en/thumb/d/d1/Find-the-X-Intercept-Step-11-Version-2.jpg/v4-728px-Find-the-X-Intercept-Step-11-Version-2.jpg)
- For example:
x=−3±32−4(−ten)2(first){displaystyle x={frac {-3pm {sqrt {3^{2}-4(-10)}}}{2(1)}}}
x=−3±32+402{displaystyle x={frac {-3pm {sqrt {3^{2}+40}}}{2}}}
![Image titled Find the X Intercept Step 12](https://www.wikihow.com/images_en/thumb/d/df/Find-the-X-Intercept-Step-12-Version-2.jpg/v4-728px-Find-the-X-Intercept-Step-12-Version-2.jpg)
- For example:
x=−3±32+402{displaystyle x={frac {-3pm {sqrt {3^{2}+40}}}{2}}}
x=−3±9+402{displaystyle x={frac {-3pm {sqrt {9+40}}}{2}}}
x=−3±492{displaystyle x={frac {-3pm {sqrt {49}}}{2}}}
![Image titled Find the X Intercept Step 13](https://www.wikihow.com/images_en/thumb/c/cd/Find-the-X-Intercept-Step-13-Version-2.jpg/v4-728px-Find-the-X-Intercept-Step-13-Version-2.jpg)
- For example:
x=−3+492{displaystyle x={frac {-3+{sqrt {49}}}{2}}}
x=−3+72{displaystyle x={frac {-3+7}{2}}}
x=42{displaystyle x={frac {4}{2}}}
x=2{displaystyle x=2}
![Image titled Find the X Intercept Step 14](https://www.wikihow.com/images_en/thumb/c/cc/Find-the-X-Intercept-Step-14-Version-2.jpg/v4-728px-Find-the-X-Intercept-Step-14-Version-2.jpg)
- For example:
x=−3−492{displaystyle x={frac {-3-{sqrt {49}}}{2}}}
x=−3−72{displaystyle x={frac {-3-7}{2}}}
x=−ten2{displaystyle x={frac {-10}{2}}}
x=−5{displaystyle x=-5}
![Image titled Find the X Intercept Step 15](https://www.wikihow.com/images_en/thumb/3/3a/Find-the-X-Intercept-Step-15-Version-2.jpg/v4-728px-Find-the-X-Intercept-Step-15-Version-2.jpg)
- For example, for the line x2+3x−ten=0{displaystyle x^{2}+3x-10=0} , the x-intersection of the function with the horizontal axis lies at the point (2,0){displaystyle(2,0)} and (−5,0){displaystyle (-5,0)} .
Advice
- If using the equation y=mx+b{displaystyle y=mx+b} , you need to know the slope of the line and the y-intersection of the function with the vertical axis. In the equation, m = slope of the line and b = the y-intersection of the function with the vertical axis. Set y equal to 0, and solve for x. You will find the x-intersection of the function with the horizontal axis.
This article was co-written by David Jia. David Jia is a tutoring teacher and founder of LA Math Tutoring, a private tutoring facility based in Los Angeles, California. With over 10 years of teaching experience, David teaches a wide variety of subjects to students of all ages and grades, as well as college admissions counseling and prep for SAT, ACT, ISEE, etc. scoring 800 in math and 690 in English on the SAT, David was awarded a Dickinson Scholarship to the University of Miami, where he graduated with a bachelor’s degree in business administration. Additionally, David has worked as an instructor in online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.
There are 7 references cited in this article that you can see at the bottom of the page.
This article has been viewed 123,628 times.
In algebra, a two-dimensional coordinate graph has a horizontal horizontal axis, also known as the x-axis, and a vertical vertical axis, also called the y-axis. Where lines representing a series of values intersect these axes is called intersection. The y-intersection of the function with the vertical axis is the point where the line intersects the y-axis, and the x-intersection of the function with the horizontal axis is where the line intersects the x-horizontal axis. For simple problems, it is easy to find the x-intersection of the function with the horizontal axis by looking at the graph. You can find the exact intersection by solving math problems using the equation of the line.
In conclusion, finding the x-intersection of a function with the horizontal axis involves identifying the values of x where the function equals zero. This can be done by setting the function equal to zero and solving for x. Different techniques such as factoring, completing the square, or using the quadratic formula may be used depending on the type of function. The x-intersection represents the points on the graph where the function intersects the horizontal axis, indicating the roots or zeros of the function. Having a clear understanding of these procedures allows us to analyze and interpret the behavior of various functions, enabling us to solve real-world problems and make informed mathematical decisions.
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