Question 985391
Here it is.

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{{{graph( 300, 300, -3.5, 3.5, -6.5, 4.5,
          3x^2-2x-5
)}}}


<B>Figure</B>. The parabola {{{y}}}={{{3x^2-2x-5}}} plot

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If you need to plot the parabola &nbsp;{{{y}}} = {{{ax^2 + by + c}}}, &nbsp;do it step by step:


1. &nbsp;Look in the sign of the coefficient at &nbsp;{{{x^2}}}. &nbsp;If it is positive, &nbsp;the parabola is U-form. &nbsp;If it is negative, &nbsp;the parabola is bottom-up.


2. &nbsp;Find the roots of the quadratic polynomial using the quadratic formula &nbsp;(see, &nbsp;for example, &nbsp;the lesson &nbsp;<A HREF=http://www.algebra.com/algebra/homework/quadratic/lessons/Introduction-Into-Quadratics.lesson>Introduction into Quadratic Equations</A>&nbsp; in this site). 


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It will help you to determine if the parabola intersect the x-axis and where.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(In your case the roots are &nbsp;-1&nbsp; and {{{5/3}}})


3. Find the coordinates of the vertex of the parabola. 


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The x-coordinate of the vertex is &nbsp;{{{-b/(2a)}}}. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(In your case it is &nbsp;{{{1/3}}})


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;To find the y-coordinate of the vertex, &nbsp;simply substitute the x-coordinate of the vertex into the quadratic polynomial.  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(In your case the y-coordinate is &nbsp;{{{-5.333}}})


That's all.