Question 81199
<pre>
Graph y = {{{3x^2}}} - {{{5x}}} - 9. Also find the vertex

a = 3, b = -5, c = -9

Let's find the vertex (h,k) first, where

h = {{{-b/(2a)}}} and k = {{{ah^2}}} + {{{bh}}} + {{{c}}}

and then the y-intercept (0,c)

h = {{{-(-5)/(2*3)}}} = {{{5/6}}}

k = {{{3(5/6)^2}}} + {{{-5(5/6)}}} + {{{-9}}} 

k = {{{3(25/36)}}} + {{{-25/6}}} - {{{9}}}

k = {{{25/12}}} - {{{25/6}}} - {{{9}}}

k = {{{25/12}}} - {{{50/12}}} - {{{108/12}}}

k = {{{-133/12}}} 

So the vertex is (h,k) = ({{{5/6}}}, {{{-133/12}}})

or for plotting purposes approximately (.8, -11.1)

the y-intercept (0,c) = (0,-9)

So plot the vertex and the y-intercept
      
{{{drawing(200,400,-3,4,-12,2,

   locate (.73,-10.74,o), locate(-.15,-8.7,o),    
   graph(200,400, -3,4,-12,2))}}}

Draw the left half of the parabola through the
y-intercept and bottoming out at the vertex:

{{{drawing(200,400,-3,4,-12,2,

   locate (.73,-10.74,o), locate(-.15,-8.7,o),    
   graph(200,400, -3,4,-12,2,sqrt(5/6-x)/sqrt(5/6-x)*(3x^2-5x-9)))}}}

Then draw the right half to match the left half:

{{{drawing(200,400,-3,4,-12,2,

   locate (.73,-10.74,o), locate(-.15,-8.7,o),    
   graph(200,400, -3,4,-12,2,3x^2-5x-9))}}}

Edwin</pre>