The Axis of Symmetry Equation Calculator is a tool designed to identify the axis of symmetry for any given quadratic equation. The axis of symmetry is a vertical line that divides the parabola into two mirror images, crucial for understanding the parabola’s properties and solving quadratic equations efficiently.
Formula of Axis of Symmetry Equation Calculator
To understand the calculations behind the tool, let’s look at the formulas used:
Standard Form:
If the equation is in standard form (y = ax^2 + bx + c), the axis of symmetry can be found using the formula:
x = -b / 2a.
Here, a, b, and c are the coefficients of the quadratic equation.
Vertex Form:
If the equation is written in vertex form (y = a(x – h)^2 + k), the axis of symmetry is the vertical line that passes through the vertex. In this form, the axis of symmetry is simply:
x = h.
Here, h is the x-coordinate of the vertex.
General Terms Table
| Equation (y = ax^2 + bx + c) | Axis of Symmetry (x = -b / 2a) |
|---|---|
| y = x^2 + 6x + 5 | x = -3 |
| y = 2x^2 + 8x + 6 | x = -2 |
| y = 3x^2 + 9x + 2 | x = -1.5 |
| y = 4x^2 + 12x + 9 | x = -1.5 |
| y = -x^2 – 4x + 7 | x = 2 |
| y = -2x^2 – 10x + 12 | x = 2.5 |
Example of Axis of Symmetry Equation Calculator
Let’s apply these formulas with a practical example:
Given a quadratic equation in standard form, y = 2x^2 + 4x + 1, find the axis of symmetry.
Using the formula x = -b / 2a:
x = -4 / (2*2) = -1
Therefore, the axis of symmetry for the given equation is x = -1.
Most Common FAQs
The axis of symmetry is a vertical line that divides a parabola into two equal halves, each mirroring the other.
You can find the axis of symmetry using two main formulas: x = -b / 2a for standard form equations and x = h for vertex form equations.
Understanding the axis of symmetry helps in solving quadratic equations, analyzing parabolas, and determining the vertex’s location, which is vital in various mathematical and real-life applications.
