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College Math

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Find the vertex and axis of symmetry of the graph of a function.

f(x)=x^2+6x+16

  • Math -

    f(x) = x^2+6x+16
    = x^2 +6x +9 +3
    = (x+3)^2 +3

    The vertex (lowest point) is x= -3, y = 3. That is because (x+3)^2 can never ne negative.
    It is symmetrical about the x=-3 vertical line.

  • College Math -

    f(x) = x^2 + 6x + 16.

    h = Xv = -b / 2a = -6 / 2 = -3,

    Substitute -3 for x in the given Eq:
    k = Yv = (-3)^2 + 6*-3 16,
    k = 9 - 18 + 16 = 25 - 18 = 7,

    V(h , k) = V(-3 , 7).

    Axis: h = Xv = -3. = A vertical line
    where x isconstant at -3 for all values of y.

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