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Math Help - Quadratic functions: related to parabolas

  1. #1
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    Quadratic functions: related to parabolas

    1) Given a quadratic function y = 2x^2 - 6x + 7, find the coordinates of the vertex by using the method of completing the square.

    2) A stone was thrown vertically upwards from the ground. Its height above the ground, s meters, reached in t seconds was given by
    s = -5t^2 + 40t

    a) Express s in the form a(t - b)^2 + c, where a, b and c are constants.
    b) What is the greatest height reached and the time to obtain this height?

    Please help and explain concepts. Thanks.
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    Quote Originally Posted by BG5965 View Post
    1) Given a quadratic function y = 2x^2 - 6x + 7, find the coordinates of the vertex by using the method of completing the square.

    Mr F says: {\color{red}y = 2\left(x^2 - 3x + \frac{7}{2}\right)}. So complete the square on {\color{red}x^2 - 3x + \frac{7}{2}} (see below) and then multiply the result the result by 2.

    2) A stone was thrown vertically upwards from the ground. Its height above the ground, s meters, reached in t seconds was given by
    s = -5t^2 + 40t

    a) Express s in the form a(t - b)^2 + c, where a, b and c are constants.

    Mr F says: {\color{red}y = -5\left(t^2 - 8t\right)}. So complete the square on {\color{red}t^2 - 8t} (see below) and then multiply the result the result by -5.

    b) What is the greatest height reached and the time to obtain this height?

    Mr F says: y-coordinate of turning point and t-coordinate of turning point.

    Please help and explain concepts. Thanks.
    Read this: Completing the Square: Solving Quadratic Equations
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