Question

How do you find the line of symmetry without using the graph?

Answer 1

Hint:We can use the formula of the quadratic equations and solve the equations by putting the values of the equation into the formula given and find the line of symmetry without using the graph method.

Complete step by step solution:
We will assume that the line of symmetry is for quadratic equations having the form of \[a{x^2} + bx + c\]
Here, \[x\] will be the vertex, and vertex \[ = - \dfrac{b}{{2a}}\]
In this, the \[x = -\dfrac{b}{{2a}}\] is called the axis of symmetry. For better understanding, we will solve an example. There is an equation, \[y = {x^2} + 2x\]. We have to find the line of symmetry without using graphs. Here, we will use the formula of quadratic equations for finding the line of symmetry.
According to our equation, \[y = {x^2} + 2x\], we get that \[a = 1;b = 2\]
Put both the values of \[a\,\,and\,\,b\] in the formula, \[x = - \dfrac{b}{{2a}}\]
\[ \Rightarrow x = -\dfrac{2}{{2 \cdot 1}}\]
After simplifying the equation, we get:
\[ \Rightarrow x = - 1\]
From this, we get that the line of symmetry is \[ - 1\]
Additional information: The line of symmetry is an imaginary line that runs through the centre of a line or shape creating two perfectly identical halves. If we find the exact centre of any object, and draw an imaginary line splitting it exactly from the centre, then we have two perfect sides of that object. Each side of this line is a perfect match. The sides look like mirror images of one another.

Note: In higher level maths, you will be asked to find the line of symmetry of a parabola. We can find the line of symmetry graphically by simply finding the farthest point of the curve of the parabola. This point is called the vertex. Vertex is a point where two points connect.