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.

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

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