Symmetry - Examples, Exercises and Solutions

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}

Suggested Topics to Practice in Advance

  1. The quadratic function
  2. Parabola
  3. Plotting the Quadratic Function Using Parameters a, b and c
  4. Finding the Zeros of a Parabola
  5. Vertex of a parabola

Practice Symmetry

Exercise #1

Given the expression of the quadratic function

Finding the symmetry point of the function

f(x)=5x2+10 f(x)=-5x^2+10

Video Solution

Answer

(0,10) (0,10)

Exercise #2

Given the expression of the quadratic function

Finding the symmetry point of the function

f(x)=2x2 f(x)=2x^2

Video Solution

Answer

(0,0) (0,0)

Exercise #3

Given the expression of the quadratic function

Finding the symmetry point of the function

f(x)=12x2 f(x)=\frac{1}{2}x^2

Video Solution

Answer

(0,0) (0,0)

Exercise #4

Given the expression of the quadratic function

The symmetrical axis of the expression must be found.

f(x)=3x2+3 f(x)=-3x^2+3

Video Solution

Answer

x=0 x=0

Exercise #5

Given the expression of the quadratic function

The symmetrical axis of the expression must be found.

f(x)=7x2 f(x)=7x^2

Video Solution

Answer

x=0 x=0

Exercise #1

Given the expression of the quadratic function

Finding the symmetry point of the function

f(x)=3x2+6x f(x)=3x^2+6x

Video Solution

Answer

(1,3) (-1,-3)

Exercise #2

Given the expression of the quadratic function

Finding the symmetry point of the function

f(x)=35x2 f(x)=3-5x^2

Video Solution

Answer

(0,3) (0,3)

Exercise #3

Given the expression of the quadratic function

Finding the symmetry point of the function

f(x)=3+3x2 f(x)=3+3x^2

Video Solution

Answer

(0,3) (0,3)

Exercise #4

A quadratic equation is graphed below.

What is the axis of symmetry for the graph f(x)=3x2+2 f(x)=3x^2+2 ?

222

Video Solution

Answer

x=0 x=0

Exercise #5

Given the expression of the quadratic function

The symmetrical axis of the expression must be found.

f(x)=4x2+6 f(x)=4x^2+6

Video Solution

Answer

x=0 x=0

Exercise #1

Calculate the axis of symmetry of the quadratic function below:

f(x)=3x2+6x6 f(x)=3x^2+6x-6

Video Solution

Answer

x=1 x=-1

Exercise #2

Given the expression of the quadratic function

Finding the symmetry point of the function

f(x)=5xx2 f(x)=5x-x^2

Video Solution

Answer

(212,614) (2\frac{1}{2},6\frac{1}{4})

Exercise #3

Given the expression of the quadratic function

Finding the symmetry point of the function

f(x)=3x2+12 f(x)=-3x^2+12

Video Solution

Answer

(0,12) (0,12)

Exercise #4

Given the expression of the quadratic function

Finding the symmetry point of the function

f(x)=4x2+8x+3 f(x)=-4x^2+8x+3

Video Solution

Answer

(1,7) (1,7)

Exercise #5

Given the expression of the quadratic function

Finding the symmetry point of the function

f(x)=6x2+24x f(x)=-6x^2+24x

Video Solution

Answer

(2,24) (2,24)