quadratic

The 'x' value of the vertex of the graph of this bowl shaped parabola  will be given by    - b / 2a    where   b = 9   a = -2

   use this value of 'x' in the equation to find the 'y' coordinate of the vertex.....

Find the vertex of the graph of the equation y = -2x^2 + 9x - 18.

Hello Guest!

\( y = -2x^2 + 9x - 18\\ y'=-4x+9=0\\ \color{blue}x_P= \frac{9}{4}\)

\( y = -2x^2 + 9x - 18\\ y=-2\cdot (2.25)^2 + 9\cdot 2.25) - 18\\ y=-10.125+20.25-18\\ \color{blue}y_P=-7.875\)

\(P_{vertex}(2.25,-7.875)\)

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