วิธีหาจุดตัด x และจุดตัด y ของสมการ

คำถาม

ง่ายมากที่จะระบุจุดตัด x และ y บนกราฟ, แต่นักเรียนมักพยายามหาพวกเขาโดยใช้สมการเท่านั้น. อย่างไรก็ตาม, แค่มีทริคง่ายๆ:

เพื่อหาจุดตัด x(NS) ของสมการ, substitute in y = 0 and solve for x.

To find the y intercept(NS) ของสมการ, substitute in x = 0 and solve for y.

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The X-Intercepts

NS x-intercepts are points where the graph of a function or an equation crosses or “touches” the x-axis of the Cartesian Plane. You may think of this as a point with y-value of zero.

  • To find the x-intercepts of an equation, let y = 0 then solve for NS.
  • In a point notation, it is written as \ซ้าย( {NS,0} \ขวา).

x-intercept of a Linear Function or a Straight Line

x-intercepts of a Quadratic การทำงาน or Parabola

The Y-Intercepts

NS y-intercepts are points where the graph of a function or an equation crosses or “touches” the y-axis of the Cartesian Plane. You may think of this as a point with x-value of zero.

  • To find the y-intercepts of an equation, let x = 0 then solve for Y.
  • In a point notation, it is written as \ซ้าย( {0,Y} \ขวา).

y-intercept of a Linear Function or a Straight Line

y-intercept of a Quadratic Function or Parabola

Examples of How to Find the x and y-intercepts of a Line, Parabola, and Circle

ตัวอย่าง 1: From the graph, describe the x and y-intercepts using point notation.

The graph crosses the x-axis at NS = 1 และ NS = 3, ดังนั้น, we can write the x-intercepts as points (1,0) และ (–3, 0).

ซึ่งเชื่อว่าจะเป็นประโยชน์ต่อการส่งมอบยาที่ต้องฉีดต่อไปในระยะยาว, the graph crosses the y-axis at Y = 3. Its y-intercept can be written as the point (0,3).


ตัวอย่าง 2: Find the x and y-intercepts of the line Y = –2NS + 4.

To find the x-intercepts algebraically, we let Y = 0 in the equation and then solve for values of NS. In the same manner, to find for y-intercepts algebraically, we let NS = 0 in the equation and then solve for Y.

Here’s the graph to verify that our answers are correct.


ตัวอย่าง 3: Find the x and y-intercepts of the quadratic equation Y = NS2 − 2NS − 3.

The graph of this quadratic equation is a parabola. We expect it to have a “U” shape where it would either open up or down.

To solve for the x-intercept of this problem, คุณจะ factor a simple trinomial. Then you set each binomial factor equal to zero and solve for x.

Our solved values for both x and y-intercepts match with the graphical solution.


ตัวอย่าง 4: Find the x and y-intercepts of the quadratic equation Y = 3NS2 + 1.

This is an example where the graph of the equation has a y-intercept but without an x-intercept.

  • Let’s find the y-intercept first because it’s extremely easy! Plug in x = 0 then solve for y.
  • Now for the x-intercept. Plug in y = 0, and solve for x.

The square root of a negative number is imaginary. This suggests that this equation does not have an x-intercept!

The graph can verify what’s going on. Notice that the graph crossed the y-axis at (0,1), but never did with the x-axis.


ตัวอย่าง 5: Find the x and y intercepts of the circle (NS + 4)2 + (Y + 2)2 = 8.

This is a good example to illustrate that it is possible for the graph of an equation to have x-intercepts but without y-intercepts.

When solving for y, we arrived at the situation of trying to get the square root of a negative number. The answer is imaginary, ดังนั้น, no solution. That means the equation doesn’t have any y-intercepts.

The graph verifies that we are right for the values of our x-intercepts, and it has no y-intercepts.

เครดิต:

https://www.studiosity.com/blog/

https://www.chilimath.com/lessons/intermediate-algebra/finding-x-y-intercepts/

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