Algebra

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Identify the vertex and the axis of symmetry for the graph of y=5(x-2)^2 + 3.

a) vertex (2,3); x = -2
b) vertex (-2,-3); x = 2
c) vertex (2,3); x = 2
d) vertex (-2,-3); x = -2

I have no idea how to solve this problem! Please help. Thank you! :)

  • Algebra -

    All parabolas of the form
    y=ax2 + bx + c
    have their axis of symmetry passing through the vertex.

    Thus a and b can be eliminated on that basis.

    Note that when the x2 term is positive, the parabola has a minimum at the vertex.

    By inspection, when x=2, the value of y is at its minimum because the 5(x-2)2 term is zero. Any other value of x will render the term > 0. Thus the vertex is at x=2, where y=3.
    Thus the answer is (C).

    Check:
    c. y=5(2-2)2+3=3
    d. y=5(-2-2)2+3=83 (not equal to 3)

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