college algebra

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graph the function and state the vertex axis of symmetry, the intercepts, if any: f(x)=x^2-8x+15


Please show work so i can understand this. thank you

  • college algebra -

    F(x) = Y = x^2 - 8x + 15.

    h = Xv = -B/2A = 8 / 2 = 4.
    K = Yv = 4^2 - 8*4 + 15 = -1.
    V(h,k) = V(4,-1).

    Axis = h = 4.

    The intercepts are the value of X when
    Y = 0:
    Y = x^2 - 8x + 15 = 0
    C = 15 = (-1)*(-15) = (-3)*(-5).
    We select -3 and -5 for factoring because the sum = B(-8).
    (x-5)(x-3) = 0
    x-5 = 0
    X = 5.
    x-3 = 0
    X = 3.
    Intercepts(Solution set): X = 5, and 3.

    To graph the function, select values of X below and above h; and calculate the
    corresponding value of Y.

    (x,y). Y = x^2 - 8x + 15.
    (1,8).
    (2,3).
    (3,0).
    V(4,-1).
    (5,0).
    (6,3).
    (7,8).

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