How To Find The Intersection With The Coordinate Axis

The intersection of the X axis is obtained by finding the random variable value x in the quadratic function if the value of variable y is zero, then the intersection point (x₁, 0) and (x₂, 0) will be obtained, where x₁ and x₂ are the roots of the equation square. But keep in mind that the roots of equations depend on discriminant.

• If D < 0, then the function does not have the roots of quadratic equations so the graph sketch of the quadratic function does not cut the X-axis.
• If D> 0, then the function has the roots of the quadratic function equation but we have difficulty solving the solution because the number that is factored is a decimal number. Where the values ​​of these roots can be obtained by the abc formula, After we get the values ​​x₁ and x₂, the intersection points of the quadratic function are (x₁, 0) and (x₂, 0)

The abc formula can be proven by the following steps,

Suppose there is an equation squared with y = 0,

ax² + bx + c = 0

First, the two segments are divided by a.

Second, the two segments are reduced by c / a.

Third, complete the perfect quadratic equation by adding the square of the half times the coefficient of x, so that later you can factor the section next to it.

Fifth, the square root of both segments.

Sixth, subtract the two sections by b / 2a.

This is the abc formula that we often use in solving quadratic equations.

• The intersection with the Y axis is obtained by finding the y value in the quadratic function if the value of the variable x is zero, so that the point (0, y₁) is obtained.

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