How to Find the Equation of the Line of Symmetry for a Parabola
A parabola is a U-shaped curve that is symmetric about a vertical line called the line of symmetry. The line of symmetry passes through the vertex of the parabola, which is the point where the parabola changes direction.
Equation of the Line of Symmetry
The equation of the line of symmetry of a parabola is given by:
x = h
- where x is the x-coordinate of any point on the line of symmetry
- and h is the x-coordinate of the vertex
Derivation of the Equation
The equation of the line of symmetry can be derived from the general form of the parabola equation:
y = a(x – h)^2 + k
- where (h, k) is the vertex of the parabola
- and a is a constant that determines the shape of the parabola
If we substitute x = h into this equation, we get:
y = a(h – h)^2 + k
y = a(0)^2 + k
y = k
This means that the line of symmetry is the vertical line passing through the point (h, k), which is the vertex of the parabola.
Examples
- For the parabola y = x^2 – 4x + 3, the vertex is (2, -1). Therefore, the equation of the line of symmetry is x = 2.
- For the parabola y = -2(x + 1)^2 + 5, the vertex is (-1, 7). Therefore, the equation of the line of symmetry is x = -1.
Conclusion
Finding the equation of the line of symmetry for a parabola is a straightforward process. By following the steps outlined in this article, you can easily determine the equation of the line of symmetry for any given parabola.
Also Read: How To Clean Piercing Holes
Recommend: What Is The Wave Like Motion Seen In Oesophagus Called How Is It Useful To Us
Related Posts: What Is The Merit Of Nda
Also Read: What Is Isgis
Recommend: How To Ask God To Heal A Broken Heart