Question

How do I find the Axis of Symmetry for a parabola

Answer 1

The equation of the axis of symmetry of the parabola is x = h,

where h is the x-coordinate of the vertex point

Explanation:

* The axis of symmetry is the line which divides the

shape into two congruent parts

* The general form of the quadratic equation is:

ax² + bx + c = 0

* The quadratic equation is represented graphically by parabola

∵ The parabola has minimum point or maximum point

∴ The axis of symmetry of the parabola is passing through this point

This point is called the vertex point or the turning point

- Lets find this point:

* the x-coordinate of this point calculated from the equation

x- coordinate of the vertex point h = -b/2a

- where b is the coefficient of x and a is the coefficient of x²

∴ The equation of the axis of symmetry of the parabola is x = -b/2a

EX:

- If ⇒ x² - 4x + 4 = 0

∵ a = 1 , b = -4

∴ h = -(-4)/2(1) = 2

∴ The equation of the axis of symmetry of the parabola is x = 2

The graph show you the axis of symmetry

Answer 2

Explanation given below.

Explanation:

The first step is to put the parabola in the form
`ax^2+bx+c` , which is the standard form of a parabola

Note: a is the coefficient before x^2 term, b is the coefficient before x term, and c is the independent constant term

The axis of symmetry divides the parabola symmetrically. The axis of symmetry has the equation
`x=-(b)/(2a)`

Where a and b are the respective values shown above

So, that is how you get the axis of symmetry of any parabola.