DETERMINE THE EQUATION OF AXIS OF SYMMETRY

What is axis of symmetry ?

The axis of symmetry is the vertical line, which divides the parabola into two equal parts.

The axis of symmetry will always pass through the vertex of the parabola.

The quadratic function

y = ax² + bx + c

will have axis of symmetry at x = -b/2a

Determine the equation of the axis of symmetry of :

Problem 1 :

y = x² + 4x + 1

Solution :

Comparing the given equation with y = ax² + bx + c

a = 1, b = 4 and c = 1

Equation of axis of symmetry x = -b/2a

x = -4/2(1)

x = -4/2

x = -2

So, equation of axis of symmetry is at x = -2.

Problem 2 :

y = 2x² - 6x + 3

Solution :

Comparing the given equation with y = ax² + bx + c

a = 2, b = -6 and c = 3

Equation of axis of symmetry x = -b/2a

x = -6/2(2)

x = -6/4

x = -3/2

Problem 3 :

y = 3x² + 4x - 1

Solution :

Comparing the given equation with y = ax² + bx + c

a = 3, b = 4 and c = -1

Equation of axis of symmetry x = -b/2a

x = -4/2(3)

x = -4/6

x = -2/3

Problem 4 :

y = -x² - 4x + 5

Solution :

Comparing the given equation with y = ax² + bx + c

a = -1, b = -4 and c = 5

Equation of axis of symmetry x = -b/2a

x = -(-4)/2(-1)

x = -4/2

x = -2

Problem 5 :

y = -2x² + 5x + 1

Solution :

Comparing the given equation with y = ax² + bx + c

a = -2, b = 5 and c = 1

Equation of axis of symmetry x = -b/2a

x = 5/2(-2)

x = -5/4

x = -2

Problem 6 :

y = (1/2)x² - 10x + 2

Solution :

Comparing the given equation with y = ax² + bx + c

a = 1/2, b = -10 and c = 2

Equation of axis of symmetry x = -b/2a

x = -(-10)/2(1/2)

x = 10

Problem 7 :

y = (1/3)x² + 4x

Solution :

Comparing the given equation with y = ax² + bx + c

a = 1/3, b = 4 and c = 0

Equation of axis of symmetry x = -b/2a

x = -4/2(1/3)

x = -4(3/2)

x = -6

Problem 8 :

y = 100x - 4x²

Solution :

y = - 4x² + 100x 

Comparing the given equation with y = ax² + bx + c

a = -4, b = 100 and c = 0

Equation of axis of symmetry x = -b/2a

x = -100/2(-4)

x = 25/2