College math

Analyze x²-6x-5y=1. Determine the vertex, focus, directrix, intercepts, axis of symmetry, and at least 2 other points on the graph.

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asked by Angel
  1. X^2 - 6X - 5Y = 1.

    Solve for Y:

    -5Y = -X^2 + 6X +1,
    Divide both sides by -5:
    Eq2: Y = X^2/5 - 6X/5 + 1/5,

    h = Xv = -b/2a = (6/5) / (2/5) = 3.

    Substitute 3 for X in Eq2:
    k = Yv = 3^2/5 - 6*3/5 + 1/5,
    k = 9/5 - 18/5 + 1/5,
    k = 9/5 - 17/5 = - 8/5 = -1 3/5.

    V(h , k) = V(3 , - 1 3/5 )

    Axis = h = 3.

    F(3 , Y2)

    V(3 , - 1 3/5)

    D(3 , Y1)


    4a = 4(1/5) = 4/5.

    1/4a = 5/4 = 1 1/4.

    Y2 = K + 1/4a,
    Y2 = - 8/5 + 5/4,
    Common denominator = 20:
    Y2 = - 32/20 + 25/20 = - 7/20.


    Y1 = K - 1/4a,
    Y1 = - 8/5 - 5/4,
    Y1 = -8/5 - 5/4,
    Common denominator = 20:
    Y1 = -32/20 - 25/20,
    Y1 = -57/20 = -2 17/20.


    F(3 , -7/20)


    V(3 , -1 3/5)

    D(3 , -2 17/20)

    P1(2 , -1 2/5)

    P2(4 , -1 2/5)

    X-Intercepts = 5.8 , 0.17.
    Use Quadratic Formula.

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    posted by Henry
  2. CORRECTION: The constant in Eq2 should
    be NEGATIVE 1/5.

    Y = X^2/5 - 6X/5 - 1/5,

    h = Xv = -b/2a = (6/5) / (2/5) = 3.

    Substitute 3 for x in Eq2:
    k=Yv=3^2/5 - 6*3/5 - 1/5 = - 10/5 =-2.

    V(h , k) = V(3 , -2).

    Axis = h = 3.

    4a = 4(1/5 = 4/5).

    1/4a = 5/4 = 1 1/4.

    F(3 , Y2)

    V(3 , -2)

    D(3 , Y1)

    Y2 = K + 1/4a = -2 + 5/4 = -3/4.

    Y1=K-1/4a = -2 - 5/4 = -13/4 = -3 1/4.

    F(3 , -3/4)

    V(3 , -2)

    D(3 , -3 3/4)

    P1(2 , -1 4/5)

    P2(4 , -1 4/5)

    X-Intercepts = 6.16 and -0.16.

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    posted by Henry

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