Axis of Symmetry Calculator

Decide the axis of symmetry for a parabola equation with the calculator. The axis of symmetry calculator suggests the complete steps concerned in calculating the vertex that divides the parabola into identical components. additionally, the device suggests a graph that higher helps to recognize the conduct of a symmetrical axis in a aircraft.

what's the Axis of Symmetry?

“Axis of symmetry is a line that passes through the parabola and divides it into halves”

The symmetrical axis is also referred to as the road of symmetry that creates a reflect photograph like the reflection on each aspect of the parabola.

Axis of Symmetry formula:

The components to calculate the axis of symmetry for parabola equation is: Axis of Symmetry Equation: \(f(x) = ax^2 + bx + c\)

Axis of Symmetry = \(X = -b / 2a\)

Steps To find AOS:

• lessen the given expression right into a standard quadratic feature shape along with:

\(ax^{2} + b x + c\)

• subsequent, pick the values of a and b (a being the coefficient of \(x^2\) and b being the coefficient of x)
• Now positioned in the values in the axis of symmetry equation that's:

\(x=\dfrac{-b}{2a}\)

• The above formula denotes that the AOS is a vertical line passing thru the subsequent factor inside the 2d aircraft:

\(\left(\dfrac{-b}{2a}, 0\right)\)

Example:

Calculate the axis of symmetry of the graph of \( y = (x - 3)^2 + 7 \) by using the formula.

Solution:

Step # 01:

Expand the given function to make a perfect quadratic function \(f(x) = (x - 3)^2 + 7\)

First, expand the squared term: \(f(x) = (x^2 - 6x + 9) + 7\)

Thus, \(f(x) = x^2 - 6x + 16\)

Step # 02:

Figure out the values of a and b in the quadratic function \(f(x) = x^2 - 6x + 16\)

Here, \(a = 1\), and \(b = -6\)

Step # 03:

Put in the values in the axis of symmetry equation to determine its value

The formula for the axis of symmetry is:

\(X = \frac{-b}{2a}\)

Substitute \(a = 1\) and \(b = -6\):

\(x = \frac{-(-6)}{2(1)}\)

\(x = \frac{6}{2}\)

\(x = 3\)

Result: Axis of symmetry = (3, 0)