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Math Help - parabola

  1. #1
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    parabola

    Place the following in standard quadratic form. (which is (x-h)+k ). The find the vertex, axis, domain, range, and zeroes.
    (can be all done with a calculator, no work needed.)



    1. f(x) = x^2-8x+16
    2. f(x)=16-x^2
    3. f(x)=x^2+4x+5
    4. f(x)= -x^2+2x+5
    5. f(x)= 4x^2-4x+21
    6. f(x)= 2x^2-x+1

    ANYONE?
    Last edited by iloveyouxD; November 24th 2008 at 06:43 PM.
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by iloveyouxD View Post
    Place the following in standard quadratic form. (which is (x-h)+k ). The find the vertex, axis, domain, range, and zeroes.
    (can be all done with a calculator, no work needed.)



    1. f(x) = x^2-8x+16
    2. f(x)=16-x^2
    3. f(x)=x^2+4x+5
    4. f(x)= -x^2+2x+5
    5. f(x)= 4x^2-4x+21
    6. f(x)= 2x^2-x+1
    I only have time to do the 1st one. Post each function individually and you may get a faster response. Good luck.

    (1) f(x)=x^2-8x+16

    f(x)=(x-4)^2+0

     V(4, 0)

    Axis of symmetry x=4

    Domain D=\{x|x \in \Re \}

    Range R=\{y|y \ge 0\}

    Zeros  x= 4 "double root"
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  3. #3
    Senior Member euclid2's Avatar
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    Quote Originally Posted by iloveyouxD View Post
    Place the following in standard quadratic form. (which is (x-h)+k ). The find the vertex, axis, domain, range, and zeroes.
    (can be all done with a calculator, no work needed.)



    1. f(x) = x^2-8x+16
    2. f(x)=16-x^2
    3. f(x)=x^2+4x+5
    4. f(x)= -x^2+2x+5
    5. f(x)= 4x^2-4x+21
    6. f(x)= 2x^2-x+1

    ANYONE?
    3.
    f(x) = x^2+4x+5
    f(x) = (x^2+4x)+5
    f(x) = (x^2+4x+4-4)+5
    f(x) = (x+2)^2 +1
    Vertex (-2,1)
    Domain, same as masters solution to 1. x is an element of real number
    Range same as masters except it is 1
    Axis=-2

    Follow the same approach for the others.
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  4. #4
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    The standard form is f(x)= ax^2+bx+c . To find the vertex find x-coordinate first using the formula x=-b/2a. The axis is the vertical line with the same x coordinate. Domain is all possible numbers of x you may use, Range is a set of all possible y you are getting by each given formula.To find 0's factor each equation and make it =0, solve it.
    I'll do #2 f(x)=16-x^2. Lets rewrite it in standard form -x^2+16, so a=-1, b=0, c=16.
    Vertex: x= -b/2a= 0. Plug x=o into y=16-x^2 to find y coordinate of the vertex:y=16, so vertex coordinates are(0,16)
    Axis: vertical line x=0(x-axis itself)
    Domain: all x's , or x is any real number.
    Range is also all real numbers( in #1you would never get negative answer, that's why y>=0)
    Zeros: Let's factor it first, -x^2+16=-1(x^2-16)= -1(x-4)(x+4). Make it =0 and solve it, x1=4, x2=-4, so zeros are (4,0), (-4,)
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