how to find x intercept from standard form

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In algebra, 2-dimensional coordinate graphs have a horizontal axis, or x-axis, and a vertical axis, or y-axis. The places where lines representing a range of values cross these axes are called intercepts. The y-intercept is the place where the line crosses the y-axis and the x-intercept where the line crosses the x-axis. For simple problems, it is easy to find the x-intercept by looking at a graph. You can find the exact point of the intercept by solving algebraically using the equation of the line.

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   Identify the x-axis. A coordinate graph has a y-axis and an x-axis. The x-axis is the horizontal line (the line that goes from left-to-right). The y-axis is the vertical line (the line that goes up and down).^[1] It is important to look at the x-axis when locating the x-intercept.

2. 2

   Find the point where the line crosses the x-axis. The x-intercept is this point.^[2] If you are asked to find the x-intercept based on the graph, the point will likely be exact (for example, at point 4). Usually, however, you will have to estimate using this method (for example, the point is somewhere between 4 and 5).

3. 3

   Write the ordered pair for the x-intercept. An ordered pair is written in the form ${\displaystyle (x,y)}$ and gives you the coordinates for the point on the line. ^[3] The first number of the pair is the point where the line crosses the x-axis (the x-intercept). The second number for will always be 0, since a point on the x-axis will never have a value for y.^[4]

   • For example, if a line crosses the x-axis at point 4, the ordered pair for the x-intercept is ${\displaystyle (4,0)}$ .

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1. 1

   Determine that the equation of the line is a quadratic equation. A quadratic equation is an equation that takes the form ${\displaystyle ax^{2}+bx+c=0}$ .^[9] A quadratic equation has two solutions, which means a line written in this form is a parabola and will have two x-intercepts.^[10]

   • For example, the equation ${\displaystyle x^{2}+3x-10=0}$ is a quadratic equation, so this line will have two x-intercepts.

2. 2

   Set up the quadratic formula. The formula is ${\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}$ , where ${\displaystyle a}$ equals the coefficient of the second-degree term ( ${\displaystyle x^{2}}$ ), ${\displaystyle b}$ equals the coefficient of the first-degree term ( ${\displaystyle x}$ ), and ${\displaystyle c}$ equals the constant.^[11]

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   Plug all of the values into the quadratic formula. Make sure you substitute the correct values for each variable from the equation of the line.

4. 4

   Simplify the equation. To do this, first complete all of the multiplication. Make sure you pay close attention to all positive and negative signs.

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   Calculate the exponent. Square the ${\displaystyle b}$ term. Then, add this number to the other number under the square root sign.

6. 6

   Solve for the addition formula. Since the quadratic formula has a ${\displaystyle \pm }$ , you will solve once by adding, and once by subtracting. Solving by adding will give you your first ${\displaystyle x}$ value.

7. 7

   Solve for the subtraction formula. This will give you the second value for ${\displaystyle x}$ . First calculate the square root, then find the difference in the numerator. Finally, divide by 2.

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• Question

  What is the x intercept?

  

  David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor's degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.

  

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• Question

  How do you find the x intercept with a line equation?

  

  David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor's degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.

  

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  If you just have a simple equation like y=mx+b, you would find the x-intercept by substituting 0 for y and solving for x. If it's a quadratic equation, you'd solve by either factoring or using the quadratic equation.

• Question

  What if the square root isnt perfect?

  

  If you mean the square root is not a whole number, that's OK. It just means that the x-intercept will occur somewhere between two integers on the x-axis.

• Question

  What is the x-intercept of the equation 2x-y=8?

  

  To find the x-intercept, set every other variable to 0, and solve for x. If 2x - 0 = 8, then 2x/2 = 8/2, and x = 4. So 4 is the x-intercept of that equation.

• Question

  What is the value of y in the equation y = 2x + 1?

  

  In order to find a numerical value for y, you would have to know the numerical value of x, then double it and add 1. Otherwise, "2x + 1" is the only value y can have.

• Question

  The graph of y=10x2+bx+c has the x intercept at 1.4 and 1.5. What is c-b?

  

  Remember that x-intercepts are roots (or zeros) of an equation, and that roots are factors. Then y = a(x-1.4)(x-1.5), where a must be 10 in order to have the leading coefficient of 10x^2. Now that you know y = 10(x-1.4)(x-1.5), just multiply it out and see what a and b are. y = 10x^2 -29x + 21. So b = -29, c = 21, and c-b = 50.

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• If you are working with the equation ${\displaystyle y=mx+b}$ , you need to know the slope of the line and the y intercept. In the equation, m = the slope of the line and b = the y-intercept. Set y to equal zero, and solve for x. This will give you your x-intercept.

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To find the x intercept using the equation of the line, plug in 0 for the y variable and solve for x. You can also use the graph of the line to find the x intercept. Just look on the graph for the point where the line crosses the x-axis, which is the horizontal axis. That point is the x intercept. To learn more, like how to find the x-intercept in a quadratic equation, keep reading the article!

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how to find x intercept from standard form

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