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Graph the quadratic functions corresponding to the following equations, and determine the roots of the equations, using technology.

  1. \(3x^2 - 9x = 0\)

    Graph \(y = 3x^2 - 9x\) using technology, and then find the \(x\)-intercepts.

    The \(x\)-intercepts of the graph are \(x = 0\) and \(x = 3\); therefore, the roots of the equation \(3x^2 - 9x = 0\) are also \(x = 0\) and \(x = 3\).


  2. \(6x^2 + 5x + 12 = 4x^2 + 15\)

    Rearrange the equation and it becomes \(2x^2 + 5x - 3 = 0\).

    Graph the function \(y = 2x^2 + 5x - 3\) using technology, and then find the \(x\)-intercepts.

    The \(x\)-intercepts of the graph are \(x = –3\) and \(x = 0.5\) or \(\frac{1}{2}\); therefore, the roots of the equation \(2x^2 + 5x - 3 = 0\) are also \(x = –3\) and \(x = 0.5\) or \(\frac{1}{2}\).




For further information about graphical solutions to quadratic equations see pp. 206 to 214 of Pre-Calculus 11.