maths

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

  1. 👍 0
  2. 👎 0
  3. 👁 618
  1. YOOOOOOOOOOOOOOOOOOOOOOO TTTTTTTTTTTTTTTTTTTTTTTTTEEEEEEEEEEEEEEEEEEENNNNNNNNNNNNNNNNNNNNNNNGGGGGGGGGGGGGGGGGGGOOOOOOOOOOOOOOOOOOOO

    1. 👍 0
    2. 👎 3

Respond to this Question

First Name

Your Response

Similar Questions

  1. algebra

    Can someone check my answers on exploring conic sections? 1. Graph x2 + y2 = 9. What are its lines of symmetry? Every line through the center is a line of symmetry. The y-axis and the x-axis are lines of symmetry.( my choice)

  2. Algebra

    graph the equation x-3=y (where do I plot the points?) find the intercepts and then graph: 5x+4y=20 find the intercepts and then graph: 1.4x-1.3y=3.64 graph the equation using slope and y-intercept: y=10/7x +4 graph using slope

  3. algebra

    Find algebraically the equation of the axis of symmetry and the coordinates of the vertex of the parabola whose equation is y= -2x-8x+3

  4. Math

    Is the dashed line a line of symmetry? *Its and Arrow with a line going throw the middle* 1) Yes 2)No

  1. Math

    What words have a horizontal line of symmetry when printed horizontally, and a vertical line of symmetry when printed vertically. The only word I have is HI.

  2. Algebra-Polynomails

    Please explain to me orgin of symmetry, y-axis semmetry, or if its neither. 1. Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. f(x) = 4x^2 - x^3 -this is how I did it:

  3. Algebra II

    Write an equation for a parabola that opens upward from its vertex at (-4,3). What is the equation of its line of symmetry?

  4. Geometry HELP!!!

    What happens to the graph of the line y = 3x -2 when the equation is changed to y = 3x +6? What happens to the graph of the line y = 2x - 5 when the equation is changed to y = 5x + 6? On the first question: What happens to the

  1. Analytic Geometry

    A line Q has an equation of x+5y+5=0. Find the equation of the line that is "perpendicular" to Q an passes through (3,1). Find the equation of the line that is "parallel" to Q and passes to through (3,1). Find the equation of the

  2. Geometry

    1.1.Determine whether the regular pentagon has reflection symmetry, rotation symmetry, both, or neither. If it has reflection symmetry, state the number of axes of symmetry. If it has rotation symmetry, state the angle of

  3. Math (Calculus) (mean value theorem emergency)

    Consider the graph of the function f(x)=x^2-x-12 a) Find the equation of the secant line joining the points (-2,-6) and (4,0). I got the equation of the secant line to be y=x-4 b) Use the Mean Value Theorem to determine a point c

  4. Algebra

    find the vertex, line of symmetry, and minimum or maxium values of the quadratic equation f(x)=9-x^2

You can view more similar questions or ask a new question.