Symmetry: Axis of symmetry

Finding a stationary point
Question 1

What is the axis of symmetry of the equation?

\( y=(x-5)^2+15 \)

Question 2

Given the expression of the quadratic function

The symmetrical axis of the expression must be found.

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

Question 3

Given the expression of the quadratic function

The symmetrical axis of the expression must be found.

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

Question 4

A quadratic equation is graphed below.

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

222

Question 5

Given the expression of the quadratic function

The symmetrical axis of the expression must be found.

\( f(x)=2x^2+8x+4 \)

Examples with solutions for Symmetry: Axis of symmetry

Exercise #1

What is the axis of symmetry of the equation?

y=(x−5)2+15 y=(x-5)^2+15

Video Solution

Step-by-Step Solution

The first step in solving the equation you presented:

y=(x-5)²+15

is to expand the parentheses:

y=x²-10x+25+15

y=x²-10x+40

From here, we can use the formula to find the X-coordinate of the vertex:

-b/2a

Let's substitute the values from the equation:

-(-10)/2*1 =

10/2=5

The axis of symmetry of the parabola is X=5

Answer

x=5 x=5

Exercise #2

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 #3

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 #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)=2x2+8x+4 f(x)=2x^2+8x+4

Video Solution

Answer

x=−2 x=-2

Question 1

Given the expression of the quadratic function

The symmetrical axis of the expression must be found.

\( f(x)=-2x^2+16 \)

Question 2

Calculate the axis of symmetry of the quadratic function below:

\( f(x)=3x^2+6x-6 \)

Question 3

A quadratic function is graphed below.

What is the axis of symmetry for the graph \( f(x)=x^2+4x \)?

Question 4

Given the expression of the quadratic function

The symmetrical axis of the expression must be found.

\( f(x)=x^2+4x+1 \)

Question 5

Given the expression of the quadratic function

The symmetrical axis of the expression must be found.

\( f(x)=-5x^2-25x \)

Exercise #6

Given the expression of the quadratic function

The symmetrical axis of the expression must be found.

f(x)=−2x2+16 f(x)=-2x^2+16

Video Solution

Answer

x=0 x=0

Exercise #7

Calculate the axis of symmetry of the quadratic function below:

f(x)=3x2+6x−6 f(x)=3x^2+6x-6

Video Solution

Answer

x=−1 x=-1

Exercise #8

A quadratic function is graphed below.

What is the axis of symmetry for the graph f(x)=x2+4x f(x)=x^2+4x ?

Video Solution

Answer

x=−2 x=-2

Exercise #9

Given the expression of the quadratic function

The symmetrical axis of the expression must be found.

f(x)=x2+4x+1 f(x)=x^2+4x+1

Video Solution

Answer

x=−2 x=-2

Exercise #10

Given the expression of the quadratic function

The symmetrical axis of the expression must be found.

f(x)=−5x2−25x f(x)=-5x^2-25x

Video Solution

Answer

x=−212 x=-2\frac{1}{2}