The axis of symmetry for a quadratic equation in standard form (y = ax² + bx + c) can be found using a specific formula derived from the properties of parabolas.
Finding the Axis of Symmetry
The axis of symmetry is a vertical line that divides the parabola into two symmetrical halves. The x-coordinate of the vertex of the parabola gives the equation of this line.
According to the provided reference (YouTube video "How to Find The Axis of Symmetry"), the formula to find the axis of symmetry is:
x = -b / 2a
Where 'a' and 'b' are the coefficients from the standard form of the quadratic equation: y = ax² + bx + c.
Steps to find the Axis of Symmetry
- Identify 'a' and 'b': From the quadratic equation in standard form (y = ax² + bx + c), identify the values of 'a' (the coefficient of x²) and 'b' (the coefficient of x).
- Apply the Formula: Substitute the values of 'a' and 'b' into the formula x = -b / 2a.
- Calculate: Simplify the expression to find the x-value. This x-value represents the equation of the vertical line that is the axis of symmetry.
Example
Let's say we have the quadratic equation y = 3x² - 12x + c.
- a = 3
- b = -12
Applying the formula:
x = -(-12) / (2 * 3) = 12 / 6 = 2
Therefore, the axis of symmetry is x = 2.
