how do i find out the the equation of the line of symmetry for
f(x)=ax^2+bx+c ?
please explain it do me thanks!
The line of symmetry runs through the vertex.
so the x of the vertex is -b/(2a)
and the equation of the line of symmetry is x = -b/(2a)
e.g. for f(x) = 2x^2 - 12x + 3
after completing the square you can find the vertex to be (3,-15)
or
the x of the vertex is -(-12)/4 = 3
then f(3) = -15.
the line of symmetry is x = 3
Quote:
The line of symmetry runs through the vertex.
so the x of the vertex is -b/(2a)
and the equation of the line of symmetry is x = -b/(2a)
why is the equation of symmetry for f(x)=ax^2+bx+c is x=-b/2a? i still don't get this...
I suspect you need to use it a couple of times, and it will sink in .
In the meantime, Memorize: for the standard quadratic, the line of symettry is -b/2a.
If you have memorized the quadratic equation, you already have it. Remember the first term in the quadratic equation?
-b/2a
The equation of the line of symmetry for the quadratic function f(x) = ax^2 + bx + c is x = -b/(2a). This formula is derived from the fact that the line of symmetry of a parabola passes through its vertex.
In a quadratic function, the x-coordinate of the vertex can be found using the formula x = -b/(2a). This equation represents the axis of symmetry, which is a vertical line that splits the parabola into two symmetrical halves.
The coefficient "a" in the quadratic function determines the shape and orientation of the parabola. If "a" is positive, the parabola opens upwards, and if "a" is negative, it opens downwards. The coefficient "b" affects the horizontal position of the vertex, while the constant term "c" determines the vertical position of the parabola.
By using the formula x = -b/(2a), you can find the x-coordinate of the vertex, and hence determine the equation of the line of symmetry.
The equation of the line of symmetry for a quadratic function in the form f(x) = ax^2 + bx + c is given by x = -b/(2a). This formula can be derived from the fact that the line of symmetry passes through the vertex of the parabola.
To understand why this formula is used, let's break it down step by step:
1. The vertex of a parabola is the point where the parabola reaches its minimum or maximum value. In the case of a quadratic function in the form f(x) = ax^2 + bx + c, the vertex can be found using the formula x = -b/(2a).
2. The x-coordinate of the vertex, denoted as h, is given by -b/(2a). This is obtained by taking the negative of the coefficient of the linear term (b) and dividing it by twice the coefficient of the quadratic term (2a).
3. Since the line of symmetry passes through the vertex, its equation can be written as x = h, where h is the x-coordinate of the vertex.
4. Simplifying x = -b/(2a), we obtain the equation of the line of symmetry as x = -b/2a.
So, to find the equation of the line of symmetry for a quadratic function, you need to compute -b/(2a), where a and b are the coefficients of the quadratic and linear terms, respectively.