Math

posted by .

find the vertex line of symmetry the minimum naximum value of the quadratic function and graph the function f(x)=-2x^2+2x+2.

  • Math -

    A parabola has either a minimum or a maximum, but not both.

    The axis of symmetry, which contains the vertex, is the line

    x = -b/2a = -2/(-4) = 1/2

    You should now be able to get the max/min and thus the vertex

  • Math -

    Express the function in canonical form by completing squares:
    if f(x)=a(x-h)²+k,
    then
    a>0 => the parabola is concave up, hence a minimum exists
    a<0 => concave down, hence a maximum.
    The location of maximum/minimum is given by the point (h,k).
    The line of symmetry is x=h.

    To proceed with completing the squares, extract and factor out the coefficient of x²:
    f(x)=-2(x²-x) + 2
    =-2[(x-1/2)²-(1/2)²]+2
    =-2[(x-1/2)²]+5/2
    So the curve is concave down, h=1/2, k=5/2 and (h,k)=(1/2,5/2) is a maximum.
    The line of symmetry is x=1/2.

  • Math -

    How do I find the Y coordinate and the x coordinates

    is the vertix 1/2, 5/2?

  • Math -

    By completing squares, we get the two parameters h and k which represent the x- and y-coordinates of the vertex.
    In this case, they are (1/2,5/2), as you can see from:
    f(x) = -2[(x-1/2)²]+5/2

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Algebra2

    Complete parts a – c for each quadratic function. a. Find the y-intercept, the equation of the axis of symmetry and the x-coordinate of the vertex. b. Make a table of values that includes the vertex. c. Use this information to graph …
  2. Algebra2

    Complete parts a – c for each quadratic function: a. Find the y-intercept, the equation of the axis of symmetry and the x- coordinate of the vertex. b. Make a table of values that includes the vertex. c. Use this information to graph …
  3. math

    find the vertex, the line of symmetry and the maximum or minimum value of f(x). graph the function. f(x)=-(x+6)^2-2 The vertex is The line of symmetry is x= The minimum/maximum value of f(x) is?
  4. ALGEBRA

    Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function. f(x) = -2x^2 + 2x + 9 x coordinate is y coordinate is the equation of the line of symmetry is x = Maximum/minimum of f(x) is the value, …
  5. algebra

    Find the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function f(x)=2-x^2
  6. algebra

    Find the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function f(x)=-2x^2+2x+9
  7. algebra

    find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function f(x)=x^2-4x-5
  8. Algebra

    Find the vertex, the line of symmetry, the maximum or minimum of the quadratic function, and graph the function. f(x)=x^2-4x-3 What is the vertex?
  9. math

    Find the vertex, the line of symmetry, and the maximum or minimum value of f(x). Graph the function. F(x) = 1/8 (x + 9)² +3
  10. math algebra trig

    For the graph of each function, find an equation of the line of symmetry and the coordinates of the vertex. Tell whether the value of the function at the vertex if a maximum or a minimum: a) y = -x^2 + 4x - 7; b) y = 2x^2 + 4x; c) …

More Similar Questions