Symmetry in a parabola

🏆Practice symmetry

The axis of symmetry in a parabola is the axis that passes through its vertex in such a way that if we folded the right side over the left side, both sides would appear joined.
Let's see it in an illustration:

Symmetry 1

To find the axis of symmetry, we must locate the value of X X of the vertex of the parabola or do it through the parabola's vertex formula or with the help of two symmetric points on the parabola.

Vertex Formula of the Parabola

X=b2a X=\frac{-b}{2a}

Formula for two symmetric points:

XVertex=The value of X at the first point + The value of X at the second point2 X_{Vertex}=\frac{The~value~of~X~at~the~first~point~+~The~value~of~X~at~the~second~point}{2}

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Test yourself on symmetry!


Given the expression of the quadratic function

The symmetrical axis of the expression must be found.

\( f(x)=-3x^2+3 \)

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Let's look at an example

First method: Solve for X at the vertex based on the formula.

Given the function x2+8x+5x^2+8x+5
Let's plug it into the formula and we will get:
From this it follows that, the axis of symmetry is X=8X=-8

Second method: Find the axis of symmetry based on symmetrical points.

Given the points (2,2)(2,2),(6,2)(6,2)

Let's plug them into the formula and we will get:
The axis of symmetry is X=4X=4

If you are interested in this article, you might also be interested in the following articles:

Symmetry in Trapezoids

Rotational Symmetry in Parallelograms

Symmetry of the Rhombus

In the Tutorela blog, you will find a variety of articles on mathematics.

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